A387163 Numbers k such that sigma(k) >= 3*k and A324644(k)/A324198(k) = 3.

10065440, 12794600, 22862840, 24806600, 27399680, 30692480, 33904640, 41629280, 41851040, 46803680, 54625760, 54842480, 70384160, 81915680, 83545280, 87311840, 91571480, 93964640, 95221280, 98030240, 101978240, 103527200, 106719200, 110116160, 121983680, 122904320, 137106200, 137359040, 143195360, 143638880, 144491200

Offset: 1

Author

Antti Karttunen, Aug 28 2025

Keywords

• nonn
• less
• new

Comments

This sequence contains all 3-perfect numbers (A005820) that are not multiples of three: 459818240 (= a(99)), 51001180160, and also any such hypothetical triperfects of the form 4u+2, when 2u+1 is not multiple of 3. See comments in A351458.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1268 (terms < 2^33).
• Index entries for sequences related to primorial base
• Index entries for sequences related to sigma(n)

Crossrefs

Intersection of A023197 and A387161.

Cf. A000203, A005820, A276086, A324198, A324644, A351458.

Cf. also A387165.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
is_A387163(n) = if(sigma(n)<3*n, 0, my(u=A276086(n)); (gcd(sigma(n), u)==3*gcd(n, u)));

Formula

{k | sigma(k) >= 3*k, A324644(k) = 3*A324198(k)}.