A351560 - OEIS

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

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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