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

1, 2, 3, 4, 5, 66, 7, 8, 9, 170, 66, 12, 13, 4830, 4830, 400, 170, 18, 19, 21320, 651, 22, 4830, 53808, 400, 21320, 27, 1092, 29, 274833900, 651, 32, 54285, 1802, 54285, 36, 37, 53808, 1092, 206480, 21320, 13835052, 43, 237380, 45, 274833900, 54285, 3600, 49

Offset: 1

Author

Jaroslav Krizek, May 12 2019

Keywords

• nonn

Examples

			a(6) = 66 because sigma(6) = sigma(11) = 12; 6 * 11 = 66.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A275987, A325651.

See A070242 and A325652 for number and sum of such numbers k.

Programs

Magma

[&*[k: k in[1..10000] | SumOfDivisors(k) eq SumOfDivisors(n)]: n in [1..100]];

Maple

N:= 1000: # to get a(n) before the first n with sigma(n) > N
S:= map(numtheory:-sigma, [$1..N-1]):
m:=min(select(t -> S[t]>N, [$1..N-1]))-1:
seq(convert(select(s -> S[s]=S[n], [$1..S[n]-1]),`*`), n=1..m); # Robert Israel, Jul 04 2019

Mathematica

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 *)

PARI

a(n) = {my(s=sigma(n)); prod(k=1, s, if ((sigma(k)==s), k, 1));} \\ Michel Marcus, May 12 2019