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

1,2

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.

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)

Mathematica

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

Prog

(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); };

Crossrefs

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

Sequence in context: A199111 A196350 A196353 * A166103 A327989 A192618

Adjacent sequences: A379478 A379479 A379480 * A379482 A379483 A379484

Keyword

nonn,easy,mult

Author

Antti Karttunen, Dec 27 2024

Status

approved