A045796 Numbers m = usigma(sigma(k))/k such that usigma(sigma(k)) is divisible by k.

1, 2, 2, 3, 3, 2, 5, 2, 3, 4, 2, 2, 4, 4, 2, 2, 4, 7, 4, 6, 3, 4, 5, 3, 4, 5, 4, 5, 3, 4, 4, 2, 5, 4, 6, 4, 8, 7, 6, 4, 5, 3, 2, 4, 5, 7, 7, 4, 4, 2, 9, 5, 5, 4, 8, 4, 4, 4, 8, 7, 4, 4, 4, 5, 6, 4, 8, 5, 8, 8, 6, 4, 6, 4, 5, 6, 4, 4, 4, 8, 5, 4, 6, 5, 8, 7, 5

Offset

1,2

Comments

a(n) = m values in A045795. - Donovan Johnson, Mar 12 2013

Links

Donovan Johnson, Table of n, a(n) for n = 1..100

Formula

a(n) = usigma(sigma(A045795(n)))/A045795(n).

Maple

A034448 := proc(n) local ans, i: ans := 1: for i from 1 to nops(ifactors(n)[ 2 ]) do ans := ans*(1+ifactors(n)[2][i][1]^ifactors(n)[2][i][2]): od: RETURN(ans) end: isA045795 := proc(n) if A034448(numtheory[sigma](n)) mod n = 0 then A034448(numtheory[sigma](n))/n ; else -1 ; fi ; end: A045796 := proc() local n, a : n := 2: while true do a := isA045795(n) ; if a>=0 then printf("%d, ", a) ; fi ; n := n+1: od : end: A045796() ; # R. J. Mathar, Jun 26 2007

Mathematica

s[n_] := Times @@ (1 + Power @@@ FactorInteger[DivisorSigma[1, n]])/n; s[1] = 1; Select[s /@ Range[10^6], IntegerQ] (* Amiram Eldar, Aug 26 2022 *)

Crossrefs

Cf. A000203, A034448, A045795, A061765.

Sequence in context: A167618 A211707 A303363 * A127684 A036012 A084401

Adjacent sequences: A045793 A045794 A045795 * A045797 A045798 A045799

Keyword

nonn

Author

Yasutoshi Kohmoto

Extensions

Corrected and extended by R. J. Mathar, Jun 26 2007

Missing first term added and offset corrected by Donovan Johnson, Mar 12 2013

Status

approved