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

1,3

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).

Formula

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

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

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 *)

Prog

(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); };

Crossrefs

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

Cf. also A336700.

Sequence in context: A320410 A011396 A256503 * A379581 A036791 A340513

Adjacent sequences: A379480 A379481 A379482 * A379484 A379485 A379486

Keyword

nonn

Author

Antti Karttunen, Dec 27 2024

Status

approved