A045796 - OEIS

%I #21 Aug 26 2022 05:25:25

%S 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,

%T 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,

%U 8,8,6,4,6,4,5,6,4,4,4,8,5,4,6,5,8,7,5

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

%C a(n) = m values in A045795. - _Donovan Johnson_, Mar 12 2013

%H Donovan Johnson, <a href="/A045796/b045796.txt">Table of n, a(n) for n = 1..100</a>

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

%p 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

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

%Y Cf. A000203, A034448, A045795, A061765.

%K nonn

%O 1,2

%A _Yasutoshi Kohmoto_

%E Corrected and extended by _R. J. Mathar_, Jun 26 2007

%E Missing first term added and offset corrected by _Donovan Johnson_, Mar 12 2013