A393477 - OEIS

%I #30 Mar 29 2026 22:22:15

%S 1,119807919,9534193025,9534194075,12043640675,12436160275

%N Numbers k such that sigma(k) = psi(k) + pi(k) + Omega(k)^10.

%e 119807919 is a term since sigma(119807919) = 215759232 = 199162368 + 6831239 + 5^10 = psi(119807919) + pi(119807919) + Omega(119807919)^10.

%o (PARI) dedpsi(f) = prod(k = 1, #f~, (f[k, 1]+1) * f[k, 1]^(f[k, 2]-1));

%o 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 + bigomega(f)^10, print1(k, ", "))); q = p); } \\ _Amiram Eldar_, Mar 24 2026

%Y Cf. A000203, A000720, A001615, A001222, A393162, A393163, A393123, A394260, A394312, A394315, A394402, A394403, A393550.

%K nonn,hard,more

%O 1,2

%A _S. I. Dimitrov_, Mar 24 2026

%E a(3)-a(6) from _Amiram Eldar_, Mar 25 2026