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%I #10 Oct 02 2015 10:11:41
%S 0,1,2,2,4,3,8,4,4,5,16,4,32,9,6,8,64,5,128,6,10,17,256,6,8,33,8,10,
%T 512,7,1024,16,18,65,12,6,2048,129,34,8,4096,11,8192,18,8,257,16384,
%U 10,16,9,66,34,32768,9,20,12,130,513,65536,8,131072,1025,12,32,36,19
%N Binary encoding of factorizations, alternative 2, a(n) = bef2(n);.
%C Gives same values as A048675 if the source sequence is squarefree (A048672), or there are max two prime divisors or one p with max exponent being 2 (A048623 and A048639).
%F a(1) = 0, a(n) = 1/4 * (2^(i1+e1) + 2^(i2+e2) + ... + 2^(iz+ez)) if n = p_i1^e1*p_i2^e2*...*p_iz^ez, where p_i is i-th prime. (e.g. p1=2, p2=3).
%p bef2 := proc(n) local s,d; s := 0; for d in ifactors(n)[ 2 ] do s := s + (2^(nthprime(d[ 1 ])+d[ 2 ]-2)); od; RETURN(s); end; # for nthprime see A048675
%o (PARI) a(n) = {if (n==1, return (0)); my(f = factor(n)); sum(k=1, #f~, 2^(primepi(f[k, 1])+f[k, 2]))/4;} \\ _Michel Marcus_, Oct 02 2015
%Y Cf. A048675.
%K nonn
%O 1,3
%A _Antti Karttunen_, Jul 14 1999
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