A394312 Numbers k such that sigma(k) = psi(k) + pi(k) + Omega(k)^5.

1, 2372, 7564, 10136, 39969, 40023, 55917, 61389, 69723, 13124150, 20751050, 49385450

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Example

2372 is a term since sigma(2372) = 4158 = 3564 + 351 + 3^5 = psi(2372) + pi(2372) + Omega(2372)^5.

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); print1(1, ", "); forprime(p = 3, lim, m++; for(k = q, p-1, f = factor(k); if(sigma(f) == dedpsi(f) + m + bigomega(f)^5, print1(k, ", "))); q = p); } \\ Amiram Eldar, Mar 15 2026

Crossrefs

Cf. A000203, A000720, A001615, A001222, A393162, A393163, A393123, A394260.

Sequence in context: A068282 A234328 A258520 * A232906 A241933 A045303

Adjacent sequences: A394309 A394310 A394311 * A394313 A394314 A394315

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Mar 15 2026

Status

approved