A035700 -id:A035700 - cp's OEIS frontend

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

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]

A035701 Number of partitions-into-distinct-parts of n is a multiple of 12.

Original entry on oeis.org

11, 27, 38, 41, 46, 49, 58, 59, 68, 79, 81, 110, 121, 128, 135, 142, 150, 159, 163, 165, 167, 171, 180, 181, 182, 193, 195, 202, 205, 206, 209, 211, 219, 221, 223, 231, 234, 240, 258, 268, 269, 277, 279, 284, 292, 296, 310, 313, 316, 319, 322, 327, 336, 339

Offset: 1

Olivier Gérard

nonn

Cf. A000009, A035700.

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]

A035702 Numbers k such that the numbers of partitions and partitions-into-distinct-parts of k are both multiples of 12.

Original entry on oeis.org

142, 180, 231, 268, 322, 336, 339, 374, 449, 531, 645, 648, 674, 765, 813, 815, 822, 859, 905, 982, 1182, 1249, 1252, 1380, 1398, 1442, 1478, 1479, 1641, 1668, 1749, 1752, 1914, 1949

Offset: 1

Olivier Gérard

nonn

Cf. A000009, A000041, A035700, A035701.

cp's OEIS Frontend

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

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Magma

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PARI

Sage

A035701 Number of partitions-into-distinct-parts of n is a multiple of 12.

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Author

Keywords

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

A035702 Numbers k such that the numbers of partitions and partitions-into-distinct-parts of k are both multiples of 12.

Views

Author

Keywords

Crossrefs