A325652 - OEIS

%I #18 Sep 08 2022 08:46:24

%S 1,2,3,4,5,17,7,8,9,27,17,12,13,52,52,41,27,18,19,87,52,22,52,121,41,

%T 87,27,67,29,253,52,32,115,87,115,36,37,121,67,187,87,250,43,192,45,

%U 253,115,123,49,50,253,149,87,292,253,292,136,187,121,663,61,250

%N a(n) = the sum of numbers k such that sigma(k) = sigma(n).

%C a(n)=n if n is in A211656, otherwise a(n) > n. - _Robert Israel_, Jul 04 2019

%H Robert Israel, <a href="/A325652/b325652.txt">Table of n, a(n) for n = 1..10000</a>

%e a(6) = 17 because sigma(6) = sigma(11) = 12; 6 + 11 = 17.

%p N:= 1000: # to get a(n) before the first n with sigma(n) > N

%p S:= map(numtheory:-sigma, [$1..N-1]):

%p m:=min(select(t -> S[t]>N, [$1..N-1]))-1:

%p 1,seq(convert(select(s -> S[s]=S[n], [$1..S[n]-1]), `+`), n=2..m); # Robert Israel, Jul 04 2019

%t a[n_] := Block[{s = DivisorSigma[1, n]}, Sum[Boole[s == DivisorSigma[1, k]] k, {k, s}]]; Array[a, 62] (* _Giovanni Resta_, Jul 03 2019 *)

%o (Magma) [&+[k: k in[1..10000] | SumOfDivisors(k) eq SumOfDivisors(n)]: n in [1..100]]

%o (PARI) a(n) = {my(s=sigma(n)); sum(k=1, s, (sigma(k)==s)*k);} \\ _Michel Marcus_, May 12 2019

%Y Cf. A000203, A211656, A275987, A325651.

%Y See A070242 and A325653 for number and product of such numbers k.

%K nonn,look

%O 1,2

%A _Jaroslav Krizek_, May 12 2019