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.
%I A272173 #35 Sep 08 2022 08:46:16
%S A272173 3,12,24,56,72,168,144,300,312,540,384,1064,588,1056,1152,1674,1080,
%T A272173 2418,1360,3024,2368,2880,2016,5400,3038,4284,4160,6048,3300,8208,
%U A272173 4096,8316,6624,7560,7200,13832,6004,9840,9408,15660,7560,17472,8448,16296,15444,14400,10176,27776
%N A272173 Product of the sum of the divisors of n and the sum of the divisors of n-th prime.
%C A272173 Numbers that occur twice in the sequence include 7560, 816000, 2709504, 31752000. Are there infinitely many? Does any number occur more than twice? - _Robert Israel_, Sep 12 2018
%H A272173 Robert Israel, <a href="/A272173/b272173.txt">Table of n, a(n) for n = 1..10000</a>
%F A272173 a(n) = sigma(n)*sigma(prime(n)) = sigma(n)*(1 + prime(n)) = A000203(n)*(1 + A000040(n)) = A000203(n)*A008864(n).
%F A272173 a(n) = sigma(n*prime(n)) = A000203(n*A000040(n)) = A000203(A033286(n)).
%F A272173 a(n) = A000203(n) + A272211(n).
%e A272173 For n = 9 the sum of the divisors of 9 is 1 + 3 + 9 = 13, and the 9th prime is 23, and the sum of the divisors of 23 is 1 + 23 = 24, and 13*24 = 312, so a(9) = 312.
%e A272173 On the other hand 9*23 = 207, and the sum of the divisors of 207 is 1 + 3 + 9 + 23 + 69 + 207 = 312, so a(9) = 312.
%p A272173 f:= n -> numtheory:-sigma(n)*(1+ithprime(n)):
%p A272173 map(f, [$1..100]); # _Robert Israel_, Sep 12 2018
%t A272173 Table[DivisorSigma[1, n]*DivisorSigma[1, Prime[n]], {n, 1, 50}] (* _G. C. Greubel_, Apr 27 2016 *)
%o A272173 (PARI) a(n) = sigma(n)*sigma(prime(n)); \\ _Michel Marcus_, Apr 27 2016
%o A272173 (Magma) [SumOfDivisors(n)*SumOfDivisors(NthPrime(n)): n in [1..50]]; // _Vincenzo Librandi_, Sep 13 2018
%Y A272173 Cf. A000040, A000203, A008864, A033286, A272211.
%K A272173 nonn
%O A272173 1,1
%A A272173 _Omar E. Pol_, Apr 26 2016