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A324966 Number of distinct odd prime indices of n. 13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,10
COMMENTS
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
LINKS
FORMULA
a(n) = A001221(n) - A324967(n). - Robert Israel, Mar 24 2019
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
EXAMPLE
180180 has prime indices {1,1,2,2,3,4,5,6}, so a(180180) = 3.
MAPLE
f:= proc(n) nops(select(type, map(numtheory:-pi, numtheory:-factorset(n)), odd)) end proc:
map(f, [$1..100]); # Robert Israel, Mar 24 2019
MATHEMATICA
Table[Count[If[n==1, {}, FactorInteger[n]], {_?(OddQ[PrimePi[#]]&), _}], {n, 100}]
PROG
(PARI) a(n) = my(f=factor(n)[, 1]); sum(k=1, #f, primepi(f[k]) % 2); \\ Michel Marcus, Mar 22 2019
CROSSREFS
Sequence in context: A364249 A191904 A265892 * A005090 A073490 A279907
KEYWORD
nonn,easy
AUTHOR
Gus Wiseman, Mar 21 2019
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)