A393123 Numbers k such that sigma(k) = psi(k) + pi(k) + Omega(k)^3.

1, 344, 452, 2826, 18297, 25533, 25587, 25713, 25749, 3785950, 17849625, 223210275, 262331175, 1465324625, 3147146375, 8989476475

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Example

344 is a term since sigma(344) = 660 = 528 + 68 + 4^3 = psi(344) + pi(344) + Omega(344)^3.

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)^3, print1(k, ", "))); q = p); } \\ Amiram Eldar, Mar 05 2026

Crossrefs

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

Sequence in context: A013844 A013306 A044878 * A085336 A236090 A237378

Adjacent sequences: A393120 A393121 A393122 * A393124 A393125 A393126

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Mar 05 2026

Extensions

a(14)-a(16) from Amiram Eldar, Mar 05 2026

Status

approved