A379483 a(n) is the number of trailing 1-bits in the binary representation of 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, 5, 1, 1, 2, 1, 1, 1, 1, 3, 3, 2, 1, 3, 1, 1, 1, 1, 1, 2, 2, 3, 2, 1, 3, 2, 1, 1, 2, 7, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 5, 1, 7, 1, 2, 4, 4, 1, 1, 2, 2, 1, 4, 6, 1, 3, 1, 3, 4, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 7, 4, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 6, 2, 2, 1, 7, 4, 1, 2, 1, 2, 6, 1, 2, 1, 1, 3, 1, 6, 2

Offset: 1

Author

Antti Karttunen, Dec 27 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A003961, A003973, A007814, A048673, A379222, A379482, A379483.

Cf. also A336700.

Programs

Mathematica

{1}~Join~Array[Length@ Last@ Split[IntegerDigits[#, 2]][[1 ;; -1 ;; 2]] &[
DivisorSigma[1,
  Apply[Times, Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]] ]^2] ] &,
    105, 2] (* Michael De Vlieger, Dec 27 2024 *)

PARI

A379483(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1); f[i, 2] *= 2); valuation(1+sigma(factorback(f)),2); };

Formula

a(n) = A007814(1+A379482(n)).

a(n) = A379222(A048673(n)).