A322673 a(n) = numerator of Product_{d|n} (sigma(d)/d) where sigma(k) = the sum of the divisors of k (A000203).

1, 3, 4, 21, 6, 4, 8, 315, 52, 81, 12, 49, 14, 144, 64, 9765, 18, 338, 20, 11907, 1024, 324, 24, 1225, 186, 441, 2080, 72, 30, 20736, 32, 615195, 256, 729, 2304, 753571, 38, 900, 3136, 321489, 42, 65536, 44, 11907, 21632, 1296, 48, 1177225, 456, 233523, 576

Offset: 1

Author

Jaroslav Krizek, Dec 23 2018

Keywords

• nonn
• frac

Examples

			For n=4; Product_{d|4} (sigma(d)/d) = (sigma(1)/1)*(sigma(2)/2)*(sigma(4)/4) = (1/1)*(3/2)*(7/4) = 21/8; a(4) = 21.
		

Links

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

Crossrefs

Cf. A000203, A318491, A318492, A299788 (denominator).

Programs

Magma

[Numerator(&*[&+[c: c in Divisors(d)] / d: d in Divisors(n)]): n in [1..100]];

Mathematica

Array[Numerator@ Product[DivisorSigma[1, d]/d, {d, Divisors@ #}] &, 51] (* Michael De Vlieger, Jan 19 2019 *)

PARI

a(n) = my(d=divisors(n)); numerator(prod(k=1, #d, sigma(d[k])/d[k])); \\ Michel Marcus, Dec 23 2018, May 11 2020

Formula

a(n) = n + 1 for n = primes (A000040).