A351560 a(n) is a binary representation of the primes that divide sigma(n) [the sum of divisors of n function], shown in decimal.

0, 2, 1, 8, 3, 3, 1, 6, 32, 3, 3, 9, 9, 3, 3, 1024, 3, 34, 5, 11, 1, 3, 3, 7, 1024, 11, 5, 9, 7, 3, 1, 10, 3, 3, 3, 40, 129, 7, 9, 7, 11, 3, 17, 11, 35, 3, 3, 1025, 130, 1026, 3, 9, 3, 7, 3, 7, 5, 7, 7, 11, 1025, 3, 33, 1073741824, 11, 3, 65, 11, 3, 3, 3, 38, 2049, 131, 1025, 13, 3, 11, 5, 1027, 16, 11, 11, 9, 3, 19

Offset

1,2

Comments

This is not additive sequence, but "oritive": For all coprime x, y (with gcd(x,y)=1), a(x*y) = a(x) OR a(y), where OR is bitwise-or (A003986). Compare also with A080398.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences related to binary expansion of n

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A087207(A000203(n)) = A048675(A080398(n)) = A048675(A007947(A000203(n))).

Mathematica

{0}~Join~Array[Total[2^(PrimePi[#] - 1) & /@ FactorInteger[DivisorSigma[1, #]][[All, 1]]] &, 85, 2] (* Michael De Vlieger, Feb 20 2022 *)

Prog

(PARI)
A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A351560(n) = A048675(A007947(sigma(n)));

Crossrefs

Cf. A000203, A003986, A007947, A048675, A080398, A087207, A351559 [= n AND a(n)].

Sequence in context: A286899 A123235 A176052 * A140273 A021462 A082834

Adjacent sequences: A351557 A351558 A351559 * A351561 A351562 A351563

Keyword

nonn

Author

Antti Karttunen, Feb 19 2022

Status

approved