A391763 Numbers k such that sigma(k) = psi(k) + phi(k) + omega(k)^4.

2964, 3008, 61184, 2168010, 16707584, 16986500, 43252398, 147053264, 4293853184, 68715020288

Offset

1,1

Comments

a(11), if it exists, is greater than 4*10^11. - Lyle Blosser, Jan 31 2026

Links

Table of n, a(n) for n=1..10.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A179138 A236005 A384431 * A107534 A184079 A236590

Adjacent sequences: A391760 A391761 A391762 * A391765 A391766 A391767

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Dec 19 2025

Extensions

a(8)-a(9) from Amiram Eldar, Dec 19 2025

a(10) from Lyle Blosser, Jan 31 2026

Status

approved