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A324966
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Number of distinct odd prime indices of n.
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13
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0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 0, 1, 0, 2, 1, 1, 1, 2, 1, 1, 0, 1, 0, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 1, 2, 1, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 1, 2, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 2, 1, 1, 2, 1, 0
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OFFSET
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1,10
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
If x and y are coprime then a(x*y) = a(x)+a(y). - Robert Israel, Mar 24 2019
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} x^prime(2*k-1) / (1 - x^prime(2*k-1)). - Ilya Gutkovskiy, Feb 12 2020
Additive with a(p^e) = 1 if primepi(p) is odd and 0 otherwise. - Amiram Eldar, Oct 06 2023
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EXAMPLE
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180180 has prime indices {1,1,2,2,3,4,5,6}, so a(180180) = 3.
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MAPLE
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f:= proc(n) nops(select(type, map(numtheory:-pi, numtheory:-factorset(n)), odd)) end proc:
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MATHEMATICA
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Table[Count[If[n==1, {}, FactorInteger[n]], {_?(OddQ[PrimePi[#]]&), _}], {n, 100}]
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PROG
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(PARI) a(n) = my(f=factor(n)[, 1]); sum(k=1, #f, primepi(f[k]) % 2); \\ Michel Marcus, Mar 22 2019
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CROSSREFS
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Cf. A000720, A001221, A003963, A005087, A066208, A112798, A257991, A257992, A289509, A324929, A324967.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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