A175433 a(n) = the smallest number m such that sigma(n) = m^k for any k >= 1 (sigma = A000203).

1, 3, 2, 7, 6, 12, 2, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 2, 6, 24, 60, 31, 42, 40, 56, 30, 72, 2, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 12, 68, 126, 96, 12

Offset: 1

Author

Jaroslav Krizek, May 10 2010

Keywords

• nonn

Comments

a(n) = A000203(n) ^ (1 / A175432(n)).

a(n) = A052410(A000203(n)). - Antti Karttunen, Nov 06 2017

Examples

			For n = 7, a(7) = 2 because sigma(7) = 8 = 2^3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000203, A052410, A175432.

Programs

Mathematica

Array[#^(1/Apply[GCD, FactorInteger[#][[All, -1]]]) &@ DivisorSigma[1, #] &, 105] (* Michael De Vlieger, Nov 05 2017 *)

PARI

A175433(n) = { my(s=sigma(n),m); ispower(s,,&m); if(m,m,s); }; \\ Antti Karttunen, Nov 05 2017

Extensions

Extended by Ray Chandler, Aug 20 2010