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A279789
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Number of ways to choose a constant partition of each part of a constant partition of n.
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14
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1, 1, 3, 3, 8, 3, 17, 3, 30, 12, 41, 3, 130, 3, 137, 45, 359, 3, 656, 3, 1306, 141, 2057, 3, 5446, 36, 8201, 544, 18610, 3, 34969, 3, 72385, 2061, 131081, 165, 290362, 3, 524297, 8205, 1109206, 3, 2130073, 3, 4371490, 33594, 8388617, 3, 17445321, 132, 33556496
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OFFSET
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0,3
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COMMENTS
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Also number of ways to choose a divisor d|n and then a sequence of n/d divisors of d.
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LINKS
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FORMULA
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G.f.: 1 + Sum_{k>=1} tau(k)*x^k/(1 - tau(k)*x^k). - Ilya Gutkovskiy, May 23 2019
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EXAMPLE
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The a(6)=17 twice-constant partitions are:
((6)),
((3)(3)), ((33)),
((3)(111)), ((111)(3)),
((2)(2)(2)), ((222)),
((2)(2)(11)), ((2)(11)(2)), ((11)(2)(2)),
((2)(11)(11)), ((11)(2)(11)), ((11)(11)(2)),
((1)(1)(1)(1)(1)(1)), ((11)(11)(11)), ((111)(111)), ((111111)).
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MAPLE
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with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1,
add(tau(n/d)^d, d=divisors(n)))
end:
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MATHEMATICA
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nn=20; Table[DivisorSum[n, Power[DivisorSigma[0, #], n/#]&], {n, nn}]
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PROG
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(PARI) a(n)=if(n==0, 1, sumdiv(n, d, numdiv(n/d)^d)) \\ Andrew Howroyd, Aug 26 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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