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A096111
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If n = 2^k - 1, then a(n) = k+1, otherwise a(n) = (A000523(n)+1)*a(A053645(n)).
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71
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1, 2, 2, 3, 3, 6, 6, 4, 4, 8, 8, 12, 12, 24, 24, 5, 5, 10, 10, 15, 15, 30, 30, 20, 20, 40, 40, 60, 60, 120, 120, 6, 6, 12, 12, 18, 18, 36, 36, 24, 24, 48, 48, 72, 72, 144, 144, 30, 30, 60, 60, 90, 90, 180, 180, 120, 120, 240, 240, 360, 360, 720, 720, 7, 7, 14, 14, 21, 21
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OFFSET
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0,2
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COMMENTS
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Each n > 1 occurs 2*A045778(n) times in the sequence.
If the binary indices of n (row n of A048793) are the positions 1's in its reversed binary expansion, then a(n) is the product of all binary indices of n + 1. The number of binary indices of n is A000120(n), their sum is A029931(n), and their average is A326699(n)/A326700(n). - Gus Wiseman, Jul 27 2019
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LINKS
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FORMULA
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G.f.: ( prod(k>=1, 1+k*x^(2^(k-1)) )- 1 ) / x. - Vladeta Jovovic, Nov 08 2005
a(n) is the product of the exponents in the binary expansion of 2*n + 2. - Peter Kagey, Apr 24 2016
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MAPLE
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f:= proc(n) local L;
L:= convert(2*n+2, base, 2);
convert(subs(0=NULL, zip(`*`, L, [$0..nops(L)-1])), `*`);
end proc:
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MATHEMATICA
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CoefficientList[(Product[1 + k x^(2^(k - 1)), {k, 7}] - 1)/x, x] (* Michael De Vlieger, Apr 08 2016 *)
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; Table[Times@@bpe[n+1], {n, 0, 100}] (* Gus Wiseman, Jul 26 2019 *)
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PROG
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(define (pow2? n) (and (> n 0) (zero? (A004198bi n (- n 1)))))
(PARI)
N=166; q='q+O('q^N);
gf= (prod(n=1, 1+ceil(log(N)/log(2)), 1+n*q^(2^(n-1)) ) - 1) / q;
Vec(gf)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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