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%I #16 Nov 07 2017 18:32:13
%S 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,
%T 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,
%U 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
%N a(n) = the greatest number k such that sigma(n) = m^k for any m >= 1 (sigma = A000203).
%C a(A175431(n)) = 1 for n >= 1.
%C a(A065496(n)) > 1 for n >= 1.
%C 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
%H Antti Karttunen, <a href="/A175432/b175432.txt">Table of n, a(n) for n = 1..16384</a>
%F a(n) = A052409(A000203(n)). - _N. J. A. Sloane_, Aug 19 2010
%F a(n) = log_A175433(n) [A000203(n)].
%e For n = 7, a(7) = 3 because sigma(7) = 8 = 2^3.
%t Array[Apply[GCD, FactorInteger[DivisorSigma[1, #]][[All, -1]]] &, 105] (* _Michael De Vlieger_, Nov 05 2017 *)
%o (PARI) a(n)=max(ispower(sigma(n)),1) \\ _Charles R Greathouse IV_, Feb 14 2013
%Y For locations of records see A169981.
%Y Cf. A000203, A052409, A175433.
%K nonn
%O 1,3
%A _Jaroslav Krizek_, May 10 2010
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