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 A279787 Twice-partitioned numbers where the first partition is constant. 38
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..5723 Gus Wiseman, Illustration of the first 9 terms of A279787 Gus Wiseman, Sequences enumerating triangles of integer partitions 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 Cf. A000005, A000041, A018818, A063834, A260685, A271619. Sequence in context: A356150 A222136 A339652 * A128488 A359366 A226303 Adjacent sequences: A279784 A279785 A279786 * A279788 A279789 A279790 KEYWORD nonn AUTHOR Gus Wiseman, Dec 18 2016 STATUS approved

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Last modified August 12 09:35 EDT 2024. Contains 375092 sequences. (Running on oeis4.)