A394926 Numbers k such that sigma(k) = psi(k) + tau(k) + Omega(k)^7.

341375, 3402150, 6668214, 16466406, 22998534, 39328854, 49127046, 71989494, 114448326, 130778646, 228760566, 251623014, 300613974, 382265574, 473715366, 506376006, 610890054, 686009526, 725202294, 849312726, 937496454, 1077937206, 1280433174, 1388213286, 1443736374

Offset

1,1

Comments

This sequence contains 136086*p^2 where p is prime such that gcd(136086, p) = 1 and is therefore infinite. Proof: sigma(136086*p^2) = 279984*(p^2 + p + 1) = 279984*(p^2 + p) + 48 + 279936 = psi(136086*p^2) + tau(136086*p^2) + bigomega(136086*p^2)^7. - David A. Corneth, Apr 07 2026

Is there any term other than a(1) not of this form, 2*3*37*613*p^2, with p <> {2, 3, 37, 613} ? - M. F. Hasler, Apr 08 2026

Links

Table of n, a(n) for n=1..25.

Example

341375 is a term since sigma(341375) = 426192 = 409800 + 8 + 4^7 = psi(341375) + tau(341375) + Omega(341375)^7.

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)) + numdiv(f) + bigomega(f)^7; } \\ Amiram Eldar, Apr 07 2026

Crossrefs

Cf. A000005, A000203, A001615, A001222, A394658, A394738, A394751, A394816, A394925.

Sequence in context: A236703 A178900 A159462 * A151559 A151563 A251495

Adjacent sequences: A394923 A394924 A394925 * A394927 A394928 A394929

Keyword

nonn

Author

S. I. Dimitrov, Apr 07 2026

Extensions

a(22)-a(25) from Amiram Eldar, Apr 07 2026

Status

approved