A390948 Numbers k such that sigma(k) = psi(k) + tau(k)^3 + pi(k).

2164, 2248, 8292, 16011, 54585, 64554875

Offset

1,1

Links

Table of n, a(n) for n=1..6.

Example

2164 is a term since sigma(2164) = 3794 = 3252 + 6^3 + 326 = psi(2164) + tau(2164)^3 + pi(2164).

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); forprime(p = 3, lim, m++; for(k = q, p-1, f = factor(k); if(sigma(f) == dedpsi(f) + numdiv(f)^3 + m, print1(k, ", "))); q = p); } \\ Amiram Eldar, Nov 24 2025

Crossrefs

Cf. A000005, A000203, A000720, A001615, A388001, A389855, A389856, A390947.

Sequence in context: A035872 A126831 A161998 * A020421 A203736 A251067

Adjacent sequences: A390945 A390946 A390947 * A390949 A390950 A390951

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Nov 24 2025

Extensions

a(6) from Amiram Eldar, Nov 24 2025

Status

approved