A279952 Number of primes with prime subscripts dividing n.

0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 2, 1, 0, 2, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 2, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 0, 1, 1, 0, 2, 0, 0, 2, 0, 1, 1, 0, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 0, 1, 1, 1, 2

Offset

1,15

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

G.f.: Sum_{k>=1} x^prime(prime(k))/(1 - x^prime(prime(k))).

Example

a(15) = 2 because 15 has 4 divisors {1,3,5,15} among which 2 divisors {3,5} are primes with prime subscripts.

Mathematica

Rest[nmax = 120; CoefficientList[Series[Sum[x^Prime[Prime[k]]/(1 - x^Prime[Prime[k]]), {k, 1, nmax}], {x, 0, nmax}], x]]

Prog

(PARI) x='x+O('x^120); concat([0, 0], Vec(sum(k=1, 120, x^prime(prime(k))/(1 - x^prime(prime(k)))))) \\ Indranil Ghosh, May 23 2017

Crossrefs

Cf. A001221, A006450.

Sequence in context: A353918 A305490 A113706 * A054845 A317991 A359980

Adjacent sequences: A279949 A279950 A279951 * A279953 A279954 A279955

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Dec 23 2016

Status

approved