A056848 -id:A056848 - cp's OEIS frontend

A056873 Numbers k such that k | p(k) - q(k) where p(k) = partition numbers (A000041) and q(k) = partition numbers into distinct parts (A000009).

1, 8, 11, 34, 310, 1688, 2307, 2708, 13988, 21315, 46739, 426378, 771476, 11762557, 18628390, 19841526, 24396168, 85110245

Offset: 1

Robert G. Wilson v, Sep 02 2000

No other terms below 10^8. - Max Alekseyev, Oct 12 2023

Cf. A000009, A000041, A051177, A056848, A056872, A121919. A128836, A162468, A259943.

Do[ If[ Mod[ PartitionsP[n] - PartitionsQ[n], n] == 0, Print[n]], {n, 1, 14577}]

a(10)-a(13) from Sean A. Irvine, May 12 2022

a(14)-a(18) from Max Alekseyev, Oct 12 2023

A294086 Numbers k such that k divides the number of planar partitions of k (A000219).

Original entry on oeis.org

1, 3, 6, 8, 10, 281, 382, 590, 5135, 13897, 31387, 37045, 46199, 85057

Offset: 1

Ilya Gutkovskiy, Feb 09 2018

a(15) > 10^5. - Seiichi Manyama, Feb 11 2018

Next term, if it exists, is greater than 250000. - Vaclav Kotesovec, Mar 02 2018

			281 is in the sequence because A000219(281) = 126261896396707768167577329446424334 is divisible by 281.

Eric Weisstein's World of Mathematics, Plane Partition

Cf. A000219, A051177, A056848.

pp[0] = 1; pp[n_] := pp[n] = (1/n)*Sum[pp[n-k]*DivisorSigma[2, k], {k, 1, n}]; Reap[For[n = 0; k = 1, k < 10^5, k++, If[Divisible[pp[k], k], n++; Print["a(", n, ") = ", k, "  pp(", k, ") = ", pp[k]]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Feb 11 2018 *)

a(14) from Seiichi Manyama, Feb 11 2018

A363252 a(n) = gcd(A000041(n), A000009(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 5, 2, 2, 2, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 2, 3, 2, 2, 1, 4, 2, 3, 7, 2, 3, 1, 1, 1, 1, 21, 21, 2, 1, 1, 2, 6, 14, 3, 1, 2, 1, 1, 1, 1, 2, 1, 3, 4, 4, 17, 1, 2, 1, 2, 2, 4, 1, 3, 5, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 4, 1, 1, 1, 2, 11, 2

Offset: 0

Vaclav Kotesovec, May 23 2023, inspired by Zhi-Wei Sun

nonn

Cf. A000009, A000041, A051177, A056848, A093952, A304991.

b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(
     `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
    end:
a:= n-> igcd(b(n), combinat[numbpart](n)):
seq(a(n), n=0..120);  # Alois P. Heinz, May 23 2023

Table[GCD[PartitionsP[n], PartitionsQ[n]], {n, 0, 100}]

cp's OEIS Frontend

A056873 Numbers k such that k | p(k) - q(k) where p(k) = partition numbers (A000041) and q(k) = partition numbers into distinct parts (A000009).

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A294086 Numbers k such that k divides the number of planar partitions of k (A000219).

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A363252 a(n) = gcd(A000041(n), A000009(n)).

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