A392054 Numbers k such that sigma(k) = psi(k) + pi(k) + omega(k)^5.

1, 16, 508, 1972, 3429, 3825, 26073, 26127, 180750, 33253275, 46310350, 47970050, 52658375, 2354524625, 3200376125

Offset

1,2

Links

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

Example

508 is a term since sigma(508) = 896 = 768 + 96 + 2^5 = psi(508) + pi(508) + omega(508)^5.

Mathematica

psi[k_]:=k Sum[MoebiusMu[d]^2/d, {d, Divisors[k]}]; okQ[k_]:=DivisorSigma[1, k]==psi[k]+PrimePi[k]+PrimeNu[k]^5; Select[Range[2*10^5], okQ] (* James C. McMahon, Feb 02 2026 *)

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)^5, print1(k, ", "))); q = p); } \\ Amiram Eldar, Jan 26 2026

Crossrefs

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

Sequence in context: A250400 A214624 A379894 * A322888 A291852 A301845

Adjacent sequences: A392051 A392052 A392053 * A392055 A392056 A392057

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Jan 26 2026

Extensions

a(14)-a(15) from Amiram Eldar, Jan 26 2026

Status

approved