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A342655
Number of prime factors (counted with multiplicity) in A156552(n).
5
0, 1, 1, 2, 1, 3, 1, 2, 2, 4, 1, 5, 1, 2, 2, 6, 1, 7, 1, 3, 2, 8, 1, 3, 2, 2, 2, 9, 2, 10, 1, 2, 2, 3, 3, 11, 1, 3, 2, 12, 1, 13, 1, 2, 4, 14, 1, 4, 2, 3, 1, 15, 1, 4, 1, 3, 3, 16, 1, 17, 2, 2, 3, 3, 2, 18, 2, 2, 1, 19, 2, 20, 2, 2, 2, 4, 2, 21, 1, 3, 2, 22, 3, 4, 3, 5, 4, 23, 3, 5, 2, 4, 4, 4, 2, 24, 2, 3, 2, 25, 3, 26, 1, 3
OFFSET
2,4
FORMULA
a(n) = A001222(A156552(n)).
a(n) = A342656(n) + A055396(n) - 1.
a(A003961(n)) = 1 + a(n).
a(A000040(n)) = n-1 for all n >= 1.
PROG
(PARI)
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res};
A342655(n) = bigomega(A156552(n));
CROSSREFS
Cf. also A323243, A324104, A324105, A324119, A342653 (sigma, phi, tau, omega and mu similarly permuted).
Sequence in context: A091948 A339443 A369323 * A161901 A102862 A029331
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 18 2021
STATUS
approved