A175432 a(n) = the greatest number k such that sigma(n) = m^k for any m >= 1 (sigma = A000203).

1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 2, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Jaroslav Krizek, May 10 2010

Keywords

• nonn

Comments

a(A175431(n)) = 1 for n >= 1.

a(A065496(n)) > 1 for n >= 1.

It appears that the record values in this sequence, 1, 2, 3, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, ..., is A180221 with a 1 prepended, at least through term #469. Is this a theorem? - Ray Chandler, Aug 20 2010

Examples

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

Links

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

Crossrefs

For locations of records see A169981.

Cf. A000203, A052409, A175433.

Programs

Mathematica

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

PARI

a(n)=max(ispower(sigma(n)),1) \\ Charles R Greathouse IV, Feb 14 2013

Formula

a(n) = A052409(A000203(n)). - N. J. A. Sloane, Aug 19 2010

a(n) = log_A175433(n) [A000203(n)].