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A279787
Twice-partitioned numbers where the first partition is constant.
39
1, 1, 3, 4, 10, 8, 29, 16, 64, 58, 124, 57, 469, 102, 489, 763, 1597, 298, 3858, 491, 8942, 6355, 6187, 1256, 59076, 18766, 20830, 49694, 167078, 4566, 481186, 6843, 752128, 362907, 231592, 1597802, 5951007, 21638, 790404, 2655810, 25274798, 44584, 40898731
OFFSET
0,3
FORMULA
a(n) = Sum_{d|n} A000041(n/d)^d for n > 0. - Andrew Howroyd, Aug 26 2018
EXAMPLE
The a(4)=10 twice-partitions are:
((4)), ((31)), ((22)), ((211)), ((1111)),
((2)(2)), ((2)(11)), ((11)(2)), ((11)(11)),
((1)(1)(1)(1)).
MAPLE
with(numtheory): with(combinat):
a:= proc(n) option remember; `if`(n=0, 1,
add(numbpart(n/d)^d, d=divisors(n)))
end:
seq(a(n), n=0..70); # Alois P. Heinz, Dec 20 2016
MATHEMATICA
nn=20; Table[DivisorSum[n, Power[PartitionsP[#], n/#]&], {n, nn}]
PROG
(PARI) a(n)=if(n==0, 1, sumdiv(n, d, numbpart(n/d)^d)) \\ Andrew Howroyd, Aug 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 18 2016
STATUS
approved