A387962 Numbers k such that sigma(k) = psi(k) + 2 * tau(k).

44, 60, 99, 126, 275, 343, 350, 539, 735, 1694, 1815, 1859, 2366, 2535, 3179, 3971, 4046, 4335, 5054, 5415, 5819, 7406, 7935, 9251, 10571, 11774, 12615, 13454, 14415, 15059, 18491, 19166, 20339, 20535, 23534, 24299, 25215, 25886, 27735, 30899, 30926, 33135, 38291, 39326, 40931, 42135, 48734

Offset

1,1

Comments

Includes 11*p^2, 14*p^2 and 15*p^2 for primes p coprime to 11, 14 and 15 respectively. In the first 1000 terms, the only one that is not one of those is 343.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(3) = 99 is a term because sigma(99) = 156, psi(99) = 144, tau(99) = 6 and 156 = 144 + 2*6.

Maple

filter:= proc(n) local F, t;
  F:= ifactors(n)[2];
  mul((t[1]^(t[2]+1)-1)/(t[1]-1), t=F) = n*mul((t[1]+1)/t[1], t=F) + 2* mul(t[2]+1, t=F);
end proc:
select(filter, [$1..10^6]);

Mathematica

psi[k_] := k Sum[MoebiusMu[d]^2/d, {d, Divisors[k]}]; ok[k_]:=DivisorSigma[1, k]==psi[k]+2DivisorSigma[0, k]; Select[Range[50000], ok] (* James C. McMahon, Oct 15 2025 *)

Crossrefs

Cf. A000005, A000203, A001615, A387953.

Sequence in context: A306116 A185590 A029690 * A353538 A220099 A067737

Adjacent sequences: A387959 A387960 A387961 * A387963 A387964 A387965

Keyword

nonn

Author

Robert Israel, Oct 12 2025

Status

approved