A389478 - OEIS

A389478

Numbers k such that sigma(k) = psi(k) + phi(k).

12, 56, 140, 270, 630, 992, 1672, 4180, 6426, 14384, 15824, 16256, 18810, 21584, 34544, 40964, 60102, 80104, 90882, 93496, 99484, 102856, 116116, 140296, 166624, 191862, 200260, 220616, 223938, 224536, 226144, 233740, 234234, 257140, 303212, 350740, 447678, 449442, 461900, 471510, 522522, 538902

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OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..473

EXAMPLE

12 is in the sequence since sigma(12) = 28 = 24 + 4 = psi(12) + phi(12).

MAPLE

filter:= proc(n) local F, t, s, p, ph;

F:= ifactors(n)[2];

s:= mul((t[1]^(t[2]+1)-1)/(t[1]-1), t = F);

p:= n * mul(1-1/t[1], t = F);

ph:= n * mul(1+1/t[1], t = F);

s = p + ph;

end proc:

select(filter, [$1..10^6]); # Robert Israel, Oct 09 2025

MATHEMATICA

psi[n_] := n * Times @@ (1 + 1/FactorInteger[n][[;; , 1]]); psi[1] = 1; Select[Range[600000], DivisorSigma[1, #] == psi[#] + EulerPhi[#] &] (* Amiram Eldar, Oct 05 2025 *)

PROG

(PARI) isok(k) = my(f = factor(k)); sigma(f) == prod(k=1, #f~, (f[k, 1]+1)*f[k, 1]^(f[k, 2]-1)) + eulerphi(f); \\ Michel Marcus, Oct 09 2025

CROSSREFS

Includes A139256. Cf. A000010, A000203, A001615.

Sequence in context: A133001 A340517 A104188 * A069552 A035005 A001386

Adjacent sequences: A389475 A389476 A389477 * A389479 A389480 A389481

KEYWORD

nonn

AUTHOR

S. I. Dimitrov, Oct 05 2025

STATUS

approved