cp's OEIS Frontend

A325653 a(n) = the product of numbers k such that sigma(k) = sigma(n).

%I A325653 #18 Jul 25 2025 19:02:23
%S A325653 1,2,3,4,5,66,7,8,9,170,66,12,13,4830,4830,400,170,18,19,21320,651,22,
%T A325653 4830,53808,400,21320,27,1092,29,274833900,651,32,54285,1802,54285,36,
%U A325653 37,53808,1092,206480,21320,13835052,43,237380,45,274833900,54285,3600,49
%N A325653 a(n) = the product of numbers k such that sigma(k) = sigma(n).
%H A325653 Robert Israel, <a href="/A325653/b325653.txt">Table of n, a(n) for n = 1..10000</a>
%e A325653 a(6) = 66 because sigma(6) = sigma(11) = 12; 6 * 11 = 66.
%p A325653 N:= 1000: # to get a(n) before the first n with sigma(n) > N
%p A325653 S:= map(numtheory:-sigma, [$1..N-1]):
%p A325653 m:=min(select(t -> S[t]>N, [$1..N-1]))-1:
%p A325653 seq(convert(select(s -> S[s]=S[n], [$1..S[n]-1]),`*`), n=1..m); # _Robert Israel_, Jul 04 2019
%t A325653 a[n_] := Block[{s = DivisorSigma[1, n]}, Product[Which[s == DivisorSigma[1, k], k, True, 1], {k, s}]]; Array[a, 49] (* _Giovanni Resta_, Jul 03 2019 *)
%o A325653 (Magma) [&*[k: k in[1..10000] | SumOfDivisors(k) eq SumOfDivisors(n)]: n in [1..100]];
%o A325653 (PARI) a(n) = {my(s=sigma(n)); prod(k=1, s, if ((sigma(k)==s), k, 1));} \\ _Michel Marcus_, May 12 2019
%Y A325653 Cf. A000203, A275987, A325651.
%Y A325653 See A070242 and A325652 for number and sum of such numbers k.
%K A325653 nonn
%O A325653 1,2
%A A325653 _Jaroslav Krizek_, May 12 2019