A386610 Numbers k such that sigma(k) = psi(k) + tau(k) + pi(k) + Omega(k).

64, 132, 236, 244, 2619, 2781, 5715, 3159250, 4796050, 389908275, 392094525, 401024775, 610130375, 3133853375, 3171455125

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Example

64 is in the sequence since sigma(64) = 127 = 96 + 7 + 18 + 6 = psi(64) + tau(64) + pi(64) + Omega(64).

Prog

(PARI) dedpsi(f) = prod(k = 1, #f~, (f[k, 1]+1) * f[k, 1]^(f[k, 2]-1));
list(lim) = {my(q = 2, m = 0, f); forprime(p = 3, lim, m++; for(k = q, p-1, f = factor(k); if(sigma(f) == dedpsi(f) + numdiv(f) + bigomega(f) + m, print1(k, ", "))); q = p); } \\ Amiram Eldar, Oct 24 2025

Crossrefs

Cf. A000203 (sigma), A001615 (psi), A000005 (tau), A000720 (pi), A001222 (Omega).

Cf. A386637, A388001, A389855.

Sequence in context: A252088 A211254 A252081 * A068410 A250654 A223063

Adjacent sequences: A386607 A386608 A386609 * A386611 A386612 A386613

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Oct 24 2025

Extensions

a(8)-a(15) from Amiram Eldar, Oct 24 2025

Status

approved