A048676 Binary encoding of factorizations, alternative 2, a(n) = bef2(n);.

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, 512, 7, 1024, 16, 18, 65, 12, 6, 2048, 129, 34, 8, 4096, 11, 8192, 18, 8, 257, 16384, 10, 16, 9, 66, 34, 32768, 9, 20, 12, 130, 513, 65536, 8, 131072, 1025, 12, 32, 36, 19

Offset: 1

Author

Antti Karttunen, Jul 14 1999

Keywords

• nonn

Comments

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).

Crossrefs

Cf. A048675.

Programs

Maple

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

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

Formula

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).