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
Keywords
Links
- Donovan Johnson, Table of n, a(n) for n = 1..100
Programs
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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
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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 *)
Extensions
Corrected and extended by R. J. Mathar, Jun 26 2007
Missing first term added and offset corrected by Donovan Johnson, Mar 12 2013
Comments