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

Author

Yasutoshi Kohmoto

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A000203, A034448, A045795, A061765.

Programs

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 *)

Formula

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

Extensions

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

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