A387999 Numbers k such that sigma(k) = psi(k) + pi(k).

1, 92, 116, 954, 4635, 4815, 13509, 15867, 23553, 23967, 24291, 15345850, 22453450, 50303150, 50304350, 125252175, 184055775

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Example

92 is in the sequence since sigma(92) = 168 = 144 + 24 = psi(12) + phi(12).

Mathematica

q[k_] := Module[{f = FactorInteger[k]}, Times @@ f1 @@@ f == Times @@ f2 @@@ f + PrimePi[k]]; q[1] = True; Select[Range[25000], q] (* Amiram Eldar, Oct 14 2025 *)

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, print1(k, ", "))); q = p); } \\ Amiram Eldar, Oct 14 2025

Crossrefs

Cf. A000203, A000720, A001615, A067788, A387953, A389478.

Sequence in context: A065511 A252068 A046116 * A273286 A257761 A393104

Adjacent sequences: A387996 A387997 A387998 * A388000 A388001 A388002

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Oct 14 2025

Extensions

a(12)-a(17) from Amiram Eldar, Oct 14 2025

Status

approved