cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A322673 #26 Jun 09 2025 14:30:53
%S A322673 1,3,4,21,6,4,8,315,52,81,12,49,14,144,64,9765,18,338,20,11907,1024,
%T A322673 324,24,1225,186,441,2080,72,30,20736,32,615195,256,729,2304,753571,
%U A322673 38,900,3136,321489,42,65536,44,11907,21632,1296,48,1177225,456,233523,576
%N A322673 a(n) = numerator of Product_{d|n} (sigma(d)/d) where sigma(k) = the sum of the divisors of k (A000203).
%H A322673 Robert Israel, <a href="/A322673/b322673.txt">Table of n, a(n) for n = 1..10000</a>
%F A322673 a(n) = n + 1 for n = primes (A000040).
%e A322673 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.
%t A322673 Array[Numerator@ Product[DivisorSigma[1, d]/d, {d, Divisors@ #}] &, 51] (* _Michael De Vlieger_, Jan 19 2019 *)
%o A322673 (Magma) [Numerator(&*[&+[c: c in Divisors(d)] / d: d in Divisors(n)]): n in [1..100]];
%o A322673 (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
%Y A322673 Cf. A000203, A318491, A318492, A299788 (denominator).
%K A322673 nonn,frac
%O A322673 1,2
%A A322673 _Jaroslav Krizek_, Dec 23 2018