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

1,3

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

Links

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

Formula

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

For locations of records see A169981.

Cf. A000203, A052409, A175433.

Sequence in context: A128258 A104967 A098495 * A204118 A095025 A274382

Adjacent sequences: A175429 A175430 A175431 * A175433 A175434 A175435

Keyword

nonn

Author

Jaroslav Krizek, May 10 2010

Status

approved