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A295931
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Number of ways to write n in the form n = (x^y)^z where x, y, and z are positive integers.
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10
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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
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OFFSET
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1,4
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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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
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MAPLE
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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:
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MATHEMATICA
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Table[Sum[DivisorSigma[0, d], {d, Divisors[GCD@@FactorInteger[n][[All, 2]]]}], {n, 100}]
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CROSSREFS
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Cf. A000005, A007425, A052409, A052410, A089723, A093771, A175082, A277562, A281113, A284639, A294786, A294336, A294338, A295920, A295923, A295924, A295935.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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