A382789 The number of prime factors of Euler phi of the n-th primorial number, counted with multiplicity.

0, 0, 1, 3, 5, 7, 10, 14, 17, 19, 22, 25, 29, 33, 36, 38, 41, 43, 47, 50, 53, 58, 61, 63, 67, 73, 77, 80, 82, 87, 92, 96, 99, 103, 106, 109, 113, 117, 122, 124, 127, 129, 134, 137, 144, 148, 152, 156, 159, 161, 165, 169, 172, 178, 182, 190, 192, 195, 200, 204

Offset: 0

Author

Amiram Eldar, Apr 05 2025

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Partial sums of A023508.

Cf. A000010, A002110, A001222, A055768, A055769.

Programs

Mathematica

Join[{0}, Accumulate[PrimeOmega[Prime[Range[100]] - 1]]]

PARI

list(nmax) = {my(s = 0, c = 0); print1(s, ", "); forprime(p = 1, , c++; s += bigomega(p-1); print1(s, ", "); if(c == nmax, break));}

Formula

a(n) = A001222(A000010(A002110(n))).

a(n) = A001222(A005867(n)).

a(n) = Sum_{k=1..n} A023508(k).