A035942 -id:A035942 - cp's OEIS frontend

A331847 Number of compositions (ordered partitions) of n into distinct prime powers (1 excluded).

1, 0, 1, 1, 1, 3, 2, 5, 3, 11, 10, 13, 18, 19, 52, 30, 61, 77, 114, 109, 146, 260, 318, 341, 356, 631, 666, 927, 848, 1849, 1978, 2305, 2213, 3560, 4302, 4748, 5588, 6779, 13952, 9044, 15534, 16897, 25084, 20731, 29524, 34882, 49360, 50765, 55112, 106903, 83652, 128552, 106638

Offset: 0

Ilya Gutkovskiy, Jan 29 2020

nonn

			a(10) = 10 because we have [8, 2], [7, 3], [5, 3, 2], [5, 2, 3], [3, 7], [3, 5, 2], [3, 2, 5], [2, 8], [2, 5, 3] and [2, 3, 5].

Index entries for sequences related to compositions

Cf. A032020, A032021, A032022, A035942, A054685, A218396, A219107, A246655, A280195, A331843, A331844, A331845, A331846.

A020902 Number of nonisomorphic cyclic subgroups of alternating group A_n (or number of distinct orders of even permutations of n objects); number of different LCM's of partitions of n which have even number of even parts.

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 13, 16, 18, 22, 26, 30, 35, 39, 46, 51, 60, 67, 76, 84, 94, 105, 119, 133, 147, 162, 176, 196, 218, 240, 263, 286, 310, 340, 374, 409, 441, 476, 515, 559, 608, 662, 711, 762, 817, 883, 955, 1030, 1104, 1177, 1257, 1352, 1453, 1559

Offset: 0

Vladeta Jovovic

nonn

			a(8)=8 because lcm{1^8} = 1, lcm{1^4 * 2^2, 2^4} = 2, lcm{1^5 * 3^1, 1^2 * 3^2} = 3, lcm{4^2, 1^2 * 2^1 * 4^1} = 4, lcm{1^3 * 5^1} = 5, lcm{2^1 * 6^1, 1^1 * 2^2 * 3^1} = 6, lcm{1^1 * 7^1} = 7, lcm{3^1 * 5^1} = 15.

V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.

Cf. A034891.

a(n) = A009490(n-2) + A035942(n-1) + A035942(n), n > 1, a(0)=a(1)=1.

cp's OEIS Frontend

A331847 Number of compositions (ordered partitions) of n into distinct prime powers (1 excluded).

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