%I #24 Feb 20 2022 10:59:53
%S 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,
%T 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,
%U 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
%N a(n) is a binary representation of the primes that divide sigma(n) [the sum of divisors of n function], shown in decimal.
%C 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.
%H Antti Karttunen, <a href="/A351560/b351560.txt">Table of n, a(n) for n = 1..8192</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = A087207(A000203(n)) = A048675(A080398(n)) = A048675(A007947(A000203(n))).
%t {0}~Join~Array[Total[2^(PrimePi[#] - 1) & /@ FactorInteger[DivisorSigma[1, #]][[All, 1]]] &, 85, 2] (* _Michael De Vlieger_, Feb 20 2022 *)
%o (PARI)
%o A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947
%o A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
%o A351560(n) = A048675(A007947(sigma(n)));
%Y Cf. A000203, A003986, A007947, A048675, A080398, A087207, A351559 [= n AND a(n)].
%K nonn
%O 1,2
%A _Antti Karttunen_, Feb 19 2022