A175433 -id:A175433 - cp's OEIS frontend

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

Jaroslav Krizek, May 10 2010

nonn

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

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

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

For locations of records see A169981.

Cf. A000203, A052409, A175433.

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

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

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

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

cp's OEIS Frontend

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

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