A080084 Number of prime factors in the factorial of the n-th prime, counted with multiplicity.

1, 2, 5, 8, 16, 20, 29, 33, 41, 56, 60, 76, 85, 89, 98, 114, 129, 134, 151, 160, 166, 180, 192, 207, 229, 240, 244, 254, 260, 271, 308, 321, 338, 342, 369, 374, 391, 409, 418, 435, 451, 457, 484, 492, 502, 507, 541, 572, 585, 590, 601, 616, 623, 653, 674, 689

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Formula

a(n) = Sum_{m=1..n} Sum_{k=1..L} floor( p_n /(p_m)^k ), where L = ceiling( log(p_n)/log(p_m) ).

Maple

b:= proc(n) option remember; `if`(n=1, 0,
      b(n-1)+numtheory[bigomega](n))
    end:
a:= n-> b(ithprime(n)):
seq(a(n), n=1..60);  # Alois P. Heinz, Jul 05 2019

Mathematica

PrimeOmega[#!]&/@Prime[Range[60]] (* Harvey P. Dale, Nov 09 2011 *)

Crossrefs

Cf. A080085, A080086, A080087.

Sequence in context: A065618 A257548 A186413 * A065093 A361270 A360671

Adjacent sequences: A080081 A080082 A080083 * A080085 A080086 A080087

Keyword

nonn

Author

Paul D. Hanna, Jan 26 2003

Status

approved