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 A295931 Number of ways to write n in the form n = (x^y)^z where x, y, and z are positive integers. 10
 1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS By convention a(1) = 1. Values can be 1, 3, 6, 9, 10, 15, 18, 21, 27, 28, 30, 36, 45, 54, 60, 63, 84, 90, etc. - Robert G. Wilson v, Dec 10 2017 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(A175082(k)) = 1, a(A093771(k)) = 3. a(n) = Sum_{d|A052409(n)} A000005(d). EXAMPLE The a(256) = 10 ways are: (2^1)^8 (2^2)^4 (2^4)^2 (2^8)^1 (4^1)^4 (4^2)^2 (4^4)^1 (16^1)^2 (16^2)^1 (256^1)^1 MAPLE f:= proc(n) local m, d, t; m:= igcd(seq(t[2], t=ifactors(n)[2])); add(numtheory:-tau(d), d=numtheory:-divisors(m)) end proc: f(1):= 1: map(f, [\$1..100]); # Robert Israel, Dec 19 2017 MATHEMATICA Table[Sum[DivisorSigma[0, d], {d, Divisors[GCD@@FactorInteger[n][[All, 2]]]}], {n, 100}] CROSSREFS Cf. A000005, A007425, A052409, A052410, A089723, A093771, A175082, A277562, A281113, A284639, A294786, A294336, A294338, A295920, A295923, A295924, A295935. Sequence in context: A030401 A275888 A308166 * A295920 A176187 A180683 Adjacent sequences: A295928 A295929 A295930 * A295932 A295933 A295934 KEYWORD nonn AUTHOR Gus Wiseman, Nov 29 2017 STATUS approved

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Last modified January 27 01:46 EST 2023. Contains 359836 sequences. (Running on oeis4.)