A379481 Square of prime-shifted n, or equally, n squared, then prime-shifted one step towards larger primes.

1, 9, 25, 81, 49, 225, 121, 729, 625, 441, 169, 2025, 289, 1089, 1225, 6561, 361, 5625, 529, 3969, 3025, 1521, 841, 18225, 2401, 2601, 15625, 9801, 961, 11025, 1369, 59049, 4225, 3249, 5929, 50625, 1681, 4761, 7225, 35721, 1849, 27225, 2209, 13689, 30625, 7569, 2809, 164025, 14641, 21609, 9025, 23409, 3481, 140625

Offset: 1

Author

Antti Karttunen, Dec 27 2024

Keywords

• nonn
• easy
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to prime indices in the factorization of n.

Crossrefs

Cf. A000290, A003961, A016754, A048673, A111003, A337336, A378231, A379482 [= sigma(a(n))], A379484 [= A379473(a(n))].

Programs

Mathematica

{1}~Join~Array[Apply[Times, Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]] ]^2 &, 53, 2] (* Michael De Vlieger, Dec 27 2024 *)

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); };

Formula

Fully multiplicative with a(prime(i)) = prime(i+1)^2.

a(n) = A003961(n^2) = A003961(n)^2.

a(n) = A016754(A048673(n)-1).

a(n) = (1/2)*(A378231(n)+A379482(n)).

From Amiram Eldar, Dec 28 2024: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/8 (A111003).

Sum_{n>=1} (-1)^(n+1)/a(n) = 7*Pi^2/72. (End)