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A324967 Number of distinct even prime indices of n. 9
0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 2, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 2, 0, 0, 2, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 0, 1, 0, 0, 2, 0, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,21
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) - A324966(n). - Robert Israel, Mar 24 2019
G.f.: Sum_{k>=1} x^prime(2*k) / (1 - x^prime(2*k)). - Ilya Gutkovskiy, Feb 12 2020
Additive with a(p^e) = 1 if primepi(p) is even 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)), even)) end proc:
map(f, [$1..100]); # Robert Israel, Mar 24 2019
MATHEMATICA
Table[Count[If[n==1, {}, FactorInteger[n]], {_?(EvenQ[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: A179317 A330657 A307598 * A320332 A358007 A348956
KEYWORD
nonn,easy
AUTHOR
Gus Wiseman, Mar 21 2019
STATUS
approved

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)