A379484 a(n) is the highest power of 3 dividing 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, 1, 1, 1, 3, 1, 1, 1, 1, 3, 3, 1, 1, 1, 3, 1, 3, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 3, 3, 3, 1, 1, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 3, 3, 3, 3, 3, 1, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 1, 1, 1, 3, 1, 1, 3, 1, 3, 1, 1, 9, 1, 3, 3, 3, 3, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 3, 1, 1, 3

Offset

1,5

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) = A038500((q^(2e+1) - 1)/(q-1)), where q = nextprime(p) = A151800(p).

a(n) = A038500(A379482(n)).

a(n) = A379473(A379481(n)).

Mathematica

{1}~Join~Array[3^IntegerExponent[#, 3] &[
  DivisorSigma[1,
    Apply[Times, Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]]^2]] &,
105, 2] (* Michael De Vlieger, Dec 27 2024 *)

Prog

(PARI) A379484(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1); f[i, 2] *= 2); 3^valuation(sigma(factorback(f)), 3); };

Crossrefs

Cf. A038500, A151800, A379473, A379481, A379482.

Sequence in context: A271714 A049639 A046555 * A336467 A331112 A029382

Adjacent sequences: A379481 A379482 A379483 * A379485 A379486 A379487

Keyword

nonn,mult

Author

Antti Karttunen, Dec 27 2024

Status

approved