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 A175432 a(n) = the greatest number k such that sigma(n) = m^k for any m >= 1 (sigma = A000203). 6
 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 (list; graph; refs; listen; history; text; internal format)
 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

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