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

0,4

Links

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

Formula

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

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

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

Mathematica

Join[{0}, Accumulate[PrimeOmega[Prime[Range[100]] - 1]]]
Join[{0}, PrimeOmega[EulerPhi[FoldList[Times, Prime[Range[60]]]]]] (* Harvey P. Dale, Mar 28 2026 *)

Prog

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

Crossrefs

Partial sums of A023508.

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

Sequence in context: A296846 A173137 A310020 * A280433 A212986 A194170

Adjacent sequences: A382786 A382787 A382788 * A382790 A382791 A382792

Keyword

nonn,easy

Author

Amiram Eldar, Apr 05 2025

Status

approved