A378639 a(n) = sum of all m such that phi(m) divides n, where phi is the Euler totient function (A000010).

3, 16, 3, 51, 3, 64, 3, 156, 3, 49, 3, 265, 3, 16, 3, 387, 3, 202, 3, 302, 3, 85, 3, 991, 3, 16, 3, 138, 3, 190, 3, 968, 3, 16, 3, 1058, 3, 16, 3, 1240, 3, 340, 3, 419, 3, 157, 3, 2736, 3, 49, 3, 210, 3, 445, 3, 620, 3, 193, 3, 1723, 3, 16, 3, 2283, 3, 334, 3, 51, 3, 262

Offset: 1

Author

Paolo Xausa, Dec 03 2024

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000

Crossrefs

Row sums of A378638.

Cf. A000010, A319048, A362469.

Programs

Maple

f:= proc(n) local d;
  if n::odd then return 3 fi;
  3+add(convert(numtheory:-invphi(d),`+`), d = select(type,numtheory:-divisors(n),even))
end proc:
map(f, [$1..100]); # Robert Israel, Dec 05 2024

Mathematica

With[{nmax = 100}, Table[If[OddQ[n], 3, Total[PositionIndex[Divisible[n, #[[;; Max[n^2, 6]]]]][True]]], {n, nmax}] & [EulerPhi[Range[nmax^2]]]]

PARI

a(n) = vecsum(select(x->!(n % eulerphi(x)), [1..max(n^2, 6)])); \\ Michel Marcus, Dec 05 2024

Formula

a(2*k+1) = 3, for k >= 0.