A390580 Numbers k such that sigma(k) = phi(k) + tau(k)^2 + pi(k).

32, 55, 91, 341, 12869, 12937, 13073, 5789473, 5790053, 36382877, 69997229, 159411799, 386930381, 891820247, 2295668269, 4712182133, 5427983713, 7623867697, 8153633179

Offset

1,1

Links

Table of n, a(n) for n=1..19.

Example

32 is in the sequence since sigma(32) = 63 = 16 + 6^2 + 11 = phi(32) + tau(32)^2 + pi(32).

Prog

(PARI) list(lim) = {my(q = 2, m = 0, f); forprime(p = 3, lim, m++; for(k = q, p-1, f = factor(k); if(sigma(f) == eulerphi(f) + numdiv(f)^2 + m, print1(k, ", "))); q = p); } \\ Amiram Eldar, Nov 11 2025

Crossrefs

Cf. A000005, A000010, A000203, A000720, A389856.

Sequence in context: A259723 A118617 A259716 * A033907 A033549 A117478

Adjacent sequences: A390577 A390578 A390579 * A390581 A390582 A390583

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Nov 11 2025

Extensions

a(8)-a(19) from Amiram Eldar, Nov 11 2025

Status

approved