A379482 a(n) = sigma(A003961(n^2)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.

1, 13, 31, 121, 57, 403, 133, 1093, 781, 741, 183, 3751, 307, 1729, 1767, 9841, 381, 10153, 553, 6897, 4123, 2379, 871, 33883, 2801, 3991, 19531, 16093, 993, 22971, 1407, 88573, 5673, 4953, 7581, 94501, 1723, 7189, 9517, 62301, 1893, 53599, 2257, 22143, 44517, 11323, 2863, 305071, 16105, 36413, 11811, 37147, 3541

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.

Index entries for sequences related to sigma(n).

Formula

Multiplicative with a(p^e) = (q^(2e+1) - 1)/(q-1), where q = nextprime(p) = A151800(p).

a(n) = A000203(A379481(n)) = A003973(A000290(n)).

a(n) = A379223(A048673(n)).

a(n) = 2*A379481(n) - A378231(n).

Mathematica

{1}~Join~Array[DivisorSigma[1, #] &[Apply[Times, Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]] ]^2] &, 52, 2] (* Michael De Vlieger, Dec 27 2024 *)

Prog

(PARI) A379482(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1); f[i, 2] *= 2); sigma(factorback(f)); };

Crossrefs

Cf. A000290, A003973, A048673, A151800, A378231, A379223, A379481, A379483, A379484 [= A038500(a(n))].

Cf. also A337336, A337337.

Sequence in context: A179035 A007628 A335787 * A141837 A299888 A023304

Adjacent sequences: A379479 A379480 A379481 * A379483 A379484 A379485

Keyword

nonn,mult

Author

Antti Karttunen, Dec 27 2024

Status

approved