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

%I A378639 #22 Dec 06 2024 11:31:41
%S A378639 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,
%T A378639 16,3,138,3,190,3,968,3,16,3,1058,3,16,3,1240,3,340,3,419,3,157,3,
%U A378639 2736,3,49,3,210,3,445,3,620,3,193,3,1723,3,16,3,2283,3,334,3,51,3,262
%N A378639 a(n) = sum of all m such that phi(m) divides n, where phi is the Euler totient function (A000010).
%H A378639 Paolo Xausa, <a href="/A378639/b378639.txt">Table of n, a(n) for n = 1..1000</a>
%F A378639 a(2*k+1) = 3, for k >= 0.
%p A378639 f:= proc(n) local d;
%p A378639   if n::odd then return 3 fi;
%p A378639   3+add(convert(numtheory:-invphi(d),`+`), d = select(type,numtheory:-divisors(n),even))
%p A378639 end proc:
%p A378639 map(f, [$1..100]); # _Robert Israel_, Dec 05 2024
%t A378639 With[{nmax = 100}, Table[If[OddQ[n], 3, Total[PositionIndex[Divisible[n, #[[;; Max[n^2, 6]]]]][True]]], {n, nmax}] & [EulerPhi[Range[nmax^2]]]]
%o A378639 (PARI) a(n) = vecsum(select(x->!(n % eulerphi(x)), [1..max(n^2, 6)])); \\ _Michel Marcus_, Dec 05 2024
%Y A378639 Row sums of A378638.
%Y A378639 Cf. A000010, A319048, A362469.
%K A378639 nonn
%O A378639 1,1
%A A378639 _Paolo Xausa_, Dec 03 2024