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

Author

Antti Karttunen, Feb 19 2022

Keywords

• nonn

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)

Crossrefs

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

Programs

Mathematica

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

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)));

Formula

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