A393090 Numbers k such that sigma(k) = psi(k) + pi(k) + omega(k)^7.

1, 16, 30915, 1439284375, 3200409125

Offset

1,2

Links

Table of n, a(n) for n=1..5.

Example

30915 is a term since sigma(30915) = 55200 = 49680 + 3333 + 3^7 = psi(30915) + pi(30915) + omega(30915)^7.

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)^7, print1(k, ", "))); q = p); } \\ Amiram Eldar, Feb 01 2026

Crossrefs

Cf. A000203, A000720, A001615, A001221, A390234, A390235, A390236, A392053, A392054, A392909.

Sequence in context: A265618 A087518 A249971 * A221244 A280656 A265662

Adjacent sequences: A393087 A393088 A393089 * A393091 A393092 A393093

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Feb 01 2026

Extensions

a(4)-a(5) from Amiram Eldar, Feb 02 2026

Status

approved