A394926 - OEIS

%I #16 Apr 13 2026 22:55:29

%S 341375,3402150,6668214,16466406,22998534,39328854,49127046,71989494,

%T 114448326,130778646,228760566,251623014,300613974,382265574,

%U 473715366,506376006,610890054,686009526,725202294,849312726,937496454,1077937206,1280433174,1388213286,1443736374

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

%C 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

%C 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

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

%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)) + numdiv(f) + bigomega(f)^7; } \\ _Amiram Eldar_, Apr 07 2026

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

%K nonn

%O 1,1

%A _S. I. Dimitrov_, Apr 07 2026

%E a(22)-a(25) from _Amiram Eldar_, Apr 07 2026