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A379481
Square of prime-shifted n, or equally, n squared, then prime-shifted one step towards larger primes.
5
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
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
KEYWORD
nonn,easy,mult
AUTHOR
Antti Karttunen, Dec 27 2024
STATUS
approved