A391763 - OEIS

%I #17 Feb 01 2026 05:05:04

%S 2964,3008,61184,2168010,16707584,16986500,43252398,147053264,

%T 4293853184,68715020288

%N Numbers k such that sigma(k) = psi(k) + phi(k) + omega(k)^4.

%C a(11), if it exists, is greater than 4*10^11. - _Lyle Blosser_, Jan 31 2026

%e 2964 is a term since sigma(2964) = 7840 = 6720 + 864 + 4^4 = psi(2964) + phi(2964) + omega(2964)^4.

%o (PARI) isok(k) = {my(f = factor(k)); sigma(f) == prod(i=1, #f~, (f[i, 1]+1) * f[i, 1]^(f[i, 2]-1)) + eulerphi(f) + omega(f)^4; } \\ _Amiram Eldar_, Dec 19 2025

%Y Cf. A000203 (sigma), A001615 (psi), A000010 (phi), A001221 (omega), A390049, A391312, A391749.

%K nonn,hard,more

%O 1,1

%A _S. I. Dimitrov_, Dec 19 2025

%E a(8)-a(9) from _Amiram Eldar_, Dec 19 2025

%E a(10) from _Lyle Blosser_, Jan 31 2026