A124874 Number of distinct primes dividing A007408(n).

0, 1, 1, 3, 2, 3, 3, 2, 3, 4, 3, 2, 3, 2, 1, 3, 2, 4, 1, 3, 2, 5, 2, 4, 2, 1, 3, 4, 3, 5, 1, 2, 3, 2, 3, 8, 4, 4, 5, 4, 8, 6, 7, 2, 4, 6, 3, 2, 4, 3, 2, 4, 3, 4, 2, 8, 3, 3, 4, 4, 3, 3, 7, 2, 5, 9, 4, 2, 6, 7, 3, 5, 6, 4, 3, 6, 4, 6, 4, 4, 3, 3, 8, 5, 7, 4, 5

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..106

Formula

a(n) = A001221(A007408(n)).

Example

a(1) = 0 since no prime divides A007408(1) = 1,
a(2) = 1 since 3 is the only prime dividing A007408(2) = 9,
a(3) = 1 since A007408(3) = 251 is prime,
a(4) = 3 since A007408(4) = 5 * 11 * 37,
a(6) = 3 since 7, 11, 53 are the only primes dividing A007408(6) = 7^2 * 11 * 53.

Maple

seq( (nops@op)(2, (ifactors@A007408)(n)), n=1..25);

Mathematica

Table[PrimeNu[Numerator[Sum[1/k^3, {k, 1, n}]]], {n, 1, 50}] (* Amiram Eldar, Feb 09 2020 *)

Crossrefs

Cf. A001221, A007408, A124876, A124877.

Sequence in context: A054263 A308656 A178775 * A230258 A016459 A242309

Adjacent sequences: A124871 A124872 A124873 * A124875 A124876 A124877

Keyword

nonn

Author

M. F. Hasler, Nov 11 2006

Extensions

More terms from Amiram Eldar, Feb 09 2020

Status

approved