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A324852
Number of distinct prime indices of n that divide n.
11
0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 1
OFFSET
1,6
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.
LINKS
EXAMPLE
60060 has 7 prime indices {1,1,2,3,4,5,6}, all of which divide 60060, and 6 of which are distinct, so a(60060) = 6.
MAPLE
a:= n-> add(`if`(irem(n, numtheory[pi](i[1]))=0, 1, 0), i=ifactors(n)[2]):
seq(a(n), n=1..120); # Alois P. Heinz, Mar 19 2019
MATHEMATICA
Table[Count[If[n==1, {}, FactorInteger[n]], {p_, _}/; Divisible[n, PrimePi[p]]], {n, 100}]
PROG
(PARI) a(n) = {my(f = factor(n)[, 1]); sum(k=1, #f, !(n % primepi(f[k]))); } \\ Michel Marcus, Mar 19 2019
CROSSREFS
The version for all prime indices (counted with multiplicity) is A324848.
Positions of zeros are A324846.
Positions of ones are A323440.
Sequence in context: A339813 A178111 A178112 * A363854 A353967 A035169
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 18 2019
STATUS
approved