A387953 Numbers k such that sigma(k) = psi(k) + tau(k).

20, 27, 45, 150, 245, 294, 605, 726, 845, 1014, 1445, 1734, 1805, 2166, 2645, 3174, 4205, 4805, 5046, 5766, 6845, 8214, 8405, 9245, 10086, 11045, 11094, 13254, 14045, 16854, 17405, 18605, 20886, 22326, 22445, 25205, 26645, 26934, 30246, 31205, 31974, 34445, 37446, 39605, 41334, 47045, 47526, 51005

Offset

1,1

Comments

Includes 5*p^2 for any prime != 5, and 6*p^2 for any prime > 3. Is 27 the only term not of those forms? - Robert Israel, Oct 12 2025

Links

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

Example

20 is in the sequence since sigma(20) = 42 = 36 + 6 = psi(20) + tau(20).

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) + mul(t[2]+1, t=F);
end proc:
select(filter, [$1..10^5]); # Robert Israel, Oct 12 2025

Mathematica

f1[p_, e_] := (p^(e + 1) - 1)/(p - 1);
f2[p_, e_] := (p + 1)*p^(e - 1);
f3[p_, e_] := e + 1;
q[k_] := Module[{f = FactorInteger[k]}, Times @@ f1 @@@ f == Times @@ f2 @@@ f + Times @@ f3 @@@ f]; Select[Range[2, 52000], q] (* Amiram Eldar, Oct 12 2025 *)

Crossrefs

Cf. A000005, A000203, A001615, A389478.

Sequence in context: A114813 A385743 A069827 * A194674 A059617 A122146

Adjacent sequences: A387950 A387951 A387952 * A387954 A387955 A387956

Keyword

nonn

Author

S. I. Dimitrov, Oct 12 2025

Status

approved