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Smith number

In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free, the factorization is written without exponents, writing the repeated factor as many times as needed.

Mathematical definition, Properties & Overview

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Mathematical definition

51 related topics

Properties

2 related topics

Overview

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Key facts & relationships

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Author of publication
Albert Wilansky
First terms
4, 22, 27, 58, 85, 94, 121
Named after
Harold Smith (brother-in-law of Albert Wilansky)
OEIS index
A006753
Total no. of terms
infinity

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Overview

Mathematical definition

Properties

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Map overview Semantic statistics

Smith number

Nodes66
Edges65
Triples25
Avg. degree1.97
Density0.030303
Components1

How this topic connects Entity context

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Smith number

Top relations

related to External links · 10
Smith number → Archived, Brady Haran, Copeland, December, Ed, Eric, MathWorld, Numberphile, Smith Numbers, Weisstein
related to Properties · 5
Smith number → It, McDaniel, Smith, The, Two
related to Mathematical definition · 4
Smith number → For, Here, Let, Smith
Author of publication · 1
Smith number → Albert Wilansky
First terms · 1
Smith number → 4, 22, 27, 58, 85, 94, 121
Named after · 1
Smith number → Harold Smith (brother-in-law of Albert Wilansky)
OEIS index · 1
Smith number → A006753
Total no. of terms · 1
Smith number → infinity
is a · 1
Smith number → composite number for which

Important terminology Word statistics

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Important terminology

smith number numbers base 10 factorization 22 displaystyle sum prime many brother-in-law named albert wilansky harold known theory given factor

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Smith numberAuthor of publicationAlbert Wilansky1.00infobox
Smith numberFirst terms4, 22, 27, 58, 85, 94, 1211.00infobox
Smith numberNamed afterHarold Smith (brother-in-law of Albert Wilansky)1.00infobox
Smith numberOEIS indexA0067531.00infobox
Smith numberTotal no. of termsinfinity1.00infobox
Smith numberis acomposite number for which0.90text
Smith numberrelated to External linksWeisstein0.60section
Smith numberrelated to External linksEric0.60section
Smith numberrelated to External linksMathWorld0.60section
Smith numberrelated to External linksCopeland0.60section
Smith numberrelated to External linksEd0.60section
Smith numberrelated to External linksDecember0.60section

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