A027827 -id:A027827 - cp's OEIS frontend

A225323 Numbers n such that 11n is a partition number.

1, 2, 7, 16, 21, 27, 35, 57, 72, 178, 338, 415, 622, 759, 1353, 1967, 2365, 2835, 4053, 4834, 5751, 15775, 18566, 21813, 25599, 35105, 47893, 65020, 75620, 101955, 118196, 158330, 490253, 644500, 738024, 1102924, 1636757, 1864205, 2121679, 2413060, 2742487, 3535243, 8424520, 10737664, 13654376, 27709215, 31120519

Offset: 1

Omar E. Pol, May 05 2013

nonn

			2 is in the sequence because 11*2 = 22 and 22 is a partition number: p(8) = A000041(8) = 22.

Cf. A000041, A027827, A213179, A213365, A216258, A217725, A217726, A222175, A222178, A222179, A225317, A225361.

Select[PartitionsP[Range[100]], Mod[#, 11] == 0 &]/11 (* T. D. Noe, May 05 2013 *)

a(j) = A225361(j)/11.

a(11)-a(47) from R. J. Mathar, May 05 2013

A243935 Numbers m such that 5 divides A000041(m).

Original entry on oeis.org

4, 7, 9, 14, 18, 19, 23, 24, 27, 29, 34, 38, 39, 44, 49, 54, 58, 59, 61, 64, 66, 68, 69, 71, 74, 79, 82, 84, 89, 94, 97, 99, 103, 104, 109, 114, 119, 120, 124, 127, 128, 129, 130, 134, 136, 139, 140, 142, 144, 149, 154, 159, 163, 164, 165, 169, 170, 173, 174

Offset: 1

Bruno Berselli, Jun 15 2014

Bruno Berselli, Table of n, a(n) for n = 1..1000

Numbers m such that k divides A000041(m), where k is prime: A001560 (k=2), A083214 (k=3), this sequence (k=5), A243936 (k=7), A027827 (k=11), A071750 (k=13). For k composite: A237278 (k=4), A035700 (k=12).

[n: n in [1..200] | IsZero(NumberOfPartitions(n) mod 5)];

Select[Range[200], Mod[PartitionsP[#], 5] == 0 &]

is(n)=numbpart(n)%5==0 \\ Charles R Greathouse IV, Apr 08 2015

# From Peter Luschny in A000041
@CachedFunction
def A000041(n):
    if n == 0: return 1
    S = 0; J = n-1; k = 2
    while 0 <= J:
        T = A000041(J)
        S = S+T if is_odd(k//2) else S-T
        J -= k if is_odd(k) else k//2
        k += 1
    return S
[n for n in (0..200) if mod(A000041(n),5) == 0]

A071750 Numbers k such that 13 divides p(k), the k-th partition number, A000041(k).

Original entry on oeis.org

28, 62, 84, 94, 129, 136, 173, 180, 197, 213, 219, 226, 227, 237, 240, 264, 294, 311, 318, 326, 335, 338, 357, 358, 389, 418, 453, 458, 473, 482, 484, 486, 508, 529, 538, 542, 562, 600, 635, 644, 668, 670, 684, 697, 699, 713, 714, 727, 742, 747, 751, 778

Offset: 1

Benoit Cloitre, Jun 24 2002

Amiram Eldar, Table of n, a(n) for n = 1..1000

Cf. A000041, A027827, A243935 (see crossrefs).

Select[ Range[800], Mod[ PartitionsP[ # ], 13] == 0 &]

\ps800 for(n=0,600,if(polcoeff(1/eta(x),n,x)%13==0,print1(n,",")))

is(n)=numbpart(n)%13==0 \\ Charles R Greathouse IV, Apr 08 2015

Edited by Robert G. Wilson v, Jun 27 2002

A243936 Numbers m such that 7 divides A000041(m).

Original entry on oeis.org

5, 10, 11, 12, 16, 18, 19, 24, 26, 27, 33, 37, 39, 40, 41, 47, 48, 52, 53, 54, 55, 61, 68, 75, 76, 82, 83, 89, 96, 97, 103, 110, 111, 117, 124, 125, 131, 138, 140, 145, 147, 152, 159, 166, 170, 173, 177, 180, 187, 191, 194, 201, 208, 213, 215, 222, 225, 229, 232

Offset: 1

Bruno Berselli, Jun 15 2014

Bruno Berselli, Table of n, a(n) for n = 1..1000

Numbers m such that k divides A000041(m), where k is prime: A001560 (k=2), A083214 (k=3), A243935 (k=5), this sequence (k=7), A027827 (k=11), A071750 (k=13). For k composite: A237278 (k=4), A035700 (k=12).

[n: n in [1..250] | IsZero(NumberOfPartitions(n) mod 7)];

Select[Range[250], Mod[PartitionsP[#], 7] == 0 &]

is(n)=numbpart(n)%7==0 \\ Charles R Greathouse IV, Apr 08 2015

# From Peter Luschny in A000041
@CachedFunction
def A000041(n):
    if n == 0: return 1
    S = 0; J = n-1; k = 2
    while 0 <= J:
        T = A000041(J)
        S = S+T if is_odd(k//2) else S-T
        J -= k if is_odd(k) else k//2
        k += 1
    return S
[n for n in (0..250) if mod(A000041(n),7) == 0]

cp's OEIS Frontend

A225323 Numbers n such that 11n is a partition number.

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A243935 Numbers m such that 5 divides A000041(m).

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A071750 Numbers k such that 13 divides p(k), the k-th partition number, A000041(k).

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Mathematica

PARI

PARI

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A243936 Numbers m such that 7 divides A000041(m).

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Programs

Magma

Mathematica

PARI

Sage