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

1,2

Comments

The exponential version of A056550.

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

Links

Table of n, a(n) for n=1..28.

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

Example

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

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 *)

Crossrefs

Cf. A051377, A056550, A064611, A307042.

Sequence in context: A091231 A250473 A049893 * A218381 A103002 A310012

Adjacent sequences: A307040 A307041 A307042 * A307044 A307045 A307046

Keyword

nonn,more

Author

Amiram Eldar, Mar 21 2019

Status

approved