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A201025 Number of partitions of n such that the number of parts and the smallest part are not coprime. 3
0, 0, 0, 1, 1, 1, 1, 3, 4, 5, 7, 10, 12, 15, 18, 25, 30, 39, 47, 62, 74, 94, 113, 144, 173, 215, 261, 324, 390, 476, 571, 697, 832, 1004, 1196, 1439, 1706, 2038, 2409, 2868, 3380, 4001, 4702, 5550, 6504, 7645, 8938, 10478, 12218, 14277, 16612, 19363, 22481 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,8
LINKS
FORMULA
a(n) = A000041(n) - A200928(n).
EXAMPLE
a(7) = 1: [2,5];
a(8) = 3: [2,2,2,2], [4,4], [2,6];
a(9) = 4: [2,2,2,3], [3,3,3], [4,5], [2,7];
a(10) = 5: [2,2,3,3], [2,2,2,4], [3,3,4], [4,6], [2,8];
a(11) = 7: [2,3,3,3], [2,2,3,4], [3,4,4], [2,2,2,5], [3,3,5], [4,7], [2,9].
MAPLE
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-> add (b(n-i, i, 2, i), i=2..iquo(n, 2)):
seq (a(n), n=1..60);
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_] := Sum [b[n-i, i, 2, i], {i, 2, Quotient[n, 2]}]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Feb 15 2017, translated from Maple *)
CROSSREFS
Sequence in context: A159560 A288427 A030502 * A288451 A236384 A351741
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 25 2011
STATUS
approved

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Last modified March 4 16:44 EST 2024. Contains 370532 sequences. (Running on oeis4.)