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A048676
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Binary encoding of factorizations, alternative 2, a(n) = bef2(n);.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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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).
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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 isi-th prime. (e.g. p1=2, p2=3)
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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
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CROSSREFS
| Cf. A048675.
Sequence in context: A174220 A048675 A162474 * A049287 A185959 A006799
Adjacent sequences: A048673 A048674 A048675 * A048677 A048678 A048679
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen, Jul 14 1999
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