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 A379481 #20 Dec 28 2024 09:11:54
%S A379481 1,9,25,81,49,225,121,729,625,441,169,2025,289,1089,1225,6561,361,
%T A379481 5625,529,3969,3025,1521,841,18225,2401,2601,15625,9801,961,11025,
%U A379481 1369,59049,4225,3249,5929,50625,1681,4761,7225,35721,1849,27225,2209,13689,30625,7569,2809,164025,14641,21609,9025,23409,3481,140625
%N A379481 Square of prime-shifted n, or equally, n squared, then prime-shifted one step towards larger primes.
%H A379481 Antti Karttunen, <a href="/A379481/b379481.txt">Table of n, a(n) for n = 1..20000</a>
%H A379481 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%F A379481 Fully multiplicative with a(prime(i)) = prime(i+1)^2.
%F A379481 a(n) = A003961(n^2) = A003961(n)^2.
%F A379481 a(n) = A016754(A048673(n)-1).
%F A379481 a(n) = (1/2)*(A378231(n)+A379482(n)).
%F A379481 From _Amiram Eldar_, Dec 28 2024: (Start)
%F A379481 Sum_{n>=1} 1/a(n) = Pi^2/8 (A111003).
%F A379481 Sum_{n>=1} (-1)^(n+1)/a(n) = 7*Pi^2/72. (End)
%t A379481 {1}~Join~Array[Apply[Times, Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]] ]^2 &, 53, 2] (* _Michael De Vlieger_, Dec 27 2024 *)
%o A379481 (PARI) A379481(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1); f[i, 2] *= 2); factorback(f); };
%Y A379481 Cf. A000290, A003961, A016754, A048673, A111003, A337336, A378231, A379482 [= sigma(a(n))], A379484 [= A379473(a(n))].
%K A379481 nonn,easy,mult
%O A379481 1,2
%A A379481 _Antti Karttunen_, Dec 27 2024