A390235 Numbers k such that sigma(k) = psi(k) + pi(k) + omega(k)^2.

1, 16, 84, 148, 164, 14697, 24363, 24399, 24417, 792150, 19033625, 48561550, 196860075, 401024175, 2040505530

Offset

1,2

Links

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

Example

84 is a term since sigma(84) = 224 = 192 + 23 + 3^2 = psi(84) + pi(84) + omega(84)^2.

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 + omega(f)^2, print1(k, ", "))); q = p); } \\ Amiram Eldar, Jan 20 2026

Crossrefs

Cf. A000203, A000720, A001615, A001221, A390234.

Sequence in context: A231303 A218082 A159501 * A395927 A172219 A172213

Adjacent sequences: A390232 A390233 A390234 * A390236 A390237 A390238

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Jan 20 2026

Extensions

a(11)-a(15) from Amiram Eldar, Jan 20 2026

Status

approved