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A200928 Number of partitions of n such that the number of parts and the smallest part are coprime. 3
1, 2, 3, 4, 6, 10, 14, 19, 26, 37, 49, 67, 89, 120, 158, 206, 267, 346, 443, 565, 718, 908, 1142, 1431, 1785, 2221, 2749, 3394, 4175, 5128, 6271, 7652, 9311, 11306, 13687, 16538, 19931, 23977, 28776, 34470, 41203, 49173, 58559, 69625, 82630, 97913, 115816 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..400

FORMULA

a(n) = A000041(n) - A201025(n).

EXAMPLE

a(4) = 4: [1,1,1,1], [1,1,2], [1,3], [4];

a(5) = 6: [1,1,1,1,1], [1,1,1,2], [1,2,2], [1,1,3], [1,4], [5];

a(6) = 10: [1,1,1,1,1,1], [1,1,1,1,2], [1,1,2,2], [2,2,2], [1,1,1,3], [1,2,3],[3,3], [1,1,4], [1,5], [6].

MAPLE

with (combinat):

b:= proc(n, j, t, s) option remember;

      add (b(n-i, i, irem(t+1, s), s), i=j..iquo(n, 2))+

      `if`(igcd(t, s)=1, 1, 0)

    end:

a:= n-> numbpart(n-1) +`if`(n>1, 1, 0) +add (b(n-i, i, 2, i), i=2..iquo(n, 2)):

seq (a(n), n=1..50);

MATHEMATICA

b[n_, j_, t_, s_] := b[n, j, t, s] = Sum[b[n-i, i, Mod[t+1, s], s], {i, j, Quotient[n, 2]}] + If[GCD[t, s]==1, 1, 0]; a[n_] := PartitionsP[n-1] + If[n>1, 1, 0] + Sum [b[n-i, i, 2, i], {i, 2, Quotient[n, 2]}]; Table[a[n], {n, 1, 50}] (* Jean-Fran├žois Alcover, Feb 15 2017, translated from Maple *)

CROSSREFS

Cf. A000041, A199888, A201025.

Sequence in context: A121152 A229863 A215255 * A318558 A256248 A089223

Adjacent sequences:  A200925 A200926 A200927 * A200929 A200930 A200931

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 25 2011

STATUS

approved

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Last modified May 9 20:59 EDT 2021. Contains 343746 sequences. (Running on oeis4.)