A307043 Numbers n such that A307042(n) = Sum_{k=1..n} esigma(k) is divisible by n, where esigma(k) is sum of exponential divisors of k (A051377).

1, 3, 4, 8, 13, 78, 94, 481, 511, 4819, 13557, 23083, 84245, 204744, 562243, 591105, 614339, 617675, 656263, 1545716, 6370802, 34882737, 534034248, 601990019, 1153304776, 2064184733, 3570196547, 10572032882

Offset: 1

Author

Amiram Eldar, Mar 21 2019

Keywords

• nonn
• more

Comments

The exponential version of A056550.

The corresponding quotients are 1, 2, 3, 5, 8, 45, ... (see the link for more values).

Examples

			3 is in the sequence since esigma(1) + esigma(2) + esigma(3) = 1 + 2 + 3 = 6 is divisible by 3.
		

Links

• Amiram Eldar, Table of n, a(n), A307042(a(n))/a(n) for n=1..28.

Crossrefs

Cf. A051377, A056550, A064611, A307042.

Programs

Mathematica

esigma[n_] := Times @@ (Sum[ First[#]^d, {d, Divisors[Last[#]]}] & ) /@ FactorInteger[n]; seq={};s = 0; Do[s = s + esigma [n]; If[Divisible[s,n], AppendTo[seq,n]], {n, 1, 10^6}]; seq (* after Jean-François Alcover at A051377 *)