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A093802
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Number of distinct factorizations of 105*2^n.
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3
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5, 15, 36, 74, 141, 250, 426, 696, 1106, 1711, 2593, 3852, 5635, 8118, 11548, 16231, 22577, 31092, 42447, 57464, 77213, 103009, 136529, 179830, 235514, 306751, 397506, 512607, 658030, 841020, 1070490, 1357195, 1714274, 2157539, 2706174, 3383187, 4216358
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OFFSET
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0,1
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..300
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EXAMPLE
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105*A000079 is 105, 210, 420, 840, 1680, 3360, ...and there are 15 distinct factorizations of 210 so a(1) = 15.
a(0) = 5: 105*2^0 = 105 = 3*5*7 = 3*35 = 5*21 = 7*15. - Alois P. Heinz, May 26 2013
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MAPLE
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with(numtheory):
b:= proc(n, k) option remember;
`if`(n>k, 0, 1) +`if`(isprime(n), 0,
add(`if`(d>k, 0, b(n/d, d)), d=divisors(n) minus {1, n}))
end:
a:= n-> b((105*2^n)$2):
seq(a(n), n=0..50); # Alois P. Heinz, May 26 2013
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CROSSREFS
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Similar sequences: 45*A000079 => A002763, [1, 3, 9, 27, 81, 243...]*A000079 => A054225, 1*A002110 => A000110, 2*A002110 => A035098, A000142 => A076716.
Cf. A001055, A126442, A129306.
Sequence in context: A174655 A184631 A011933 * A006008 A325952 A086716
Adjacent sequences: A093799 A093800 A093801 * A093803 A093804 A093805
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KEYWORD
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easy,nonn
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AUTHOR
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Alford Arnold, May 19 2004
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EXTENSIONS
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2 more terms from Alford Arnold, Aug 29 2007
Corrected offset and extended beyond a(7) by Alois P. Heinz, May 26 2013
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STATUS
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approved
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