A328369 Numbers without repeated parts in their partitions into consecutive parts.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 78, 79, 80, 82, 83, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 100

Offset

1,2

Comments

All primes are terms. - Ivan N. Ianakiev, Nov 05 2019

All powers of 2 are terms. - Omar E. Pol, Nov 19 2019

Links

Table of n, a(n) for n=1..79.

Example

The partitions of 9 into consecutive parts are [9], [5, 4], [4, 3, 2]. The 4 is a repeated part, so 9 is not in the sequence.
The partitions of 10 into consecutive parts are [10], [4, 3, 2, 1]. There are no repeated parts, so 10 is in the sequence.

Mathematica

Array[If[Or[PrimeQ@ #, IntegerQ@ Log2@ #], #, # Boole[Count[Tally@ Flatten@ Select[IntegerPartitions[#], Union@ Differences@ # == {-1} &], _?(Last@ # > 1 &)] == 0]] /. 0 -> Nothing &, 60] (* Michael De Vlieger, Nov 22 2019 *)

Crossrefs

Cf. A001227, A118236 (complement), A286000, A286001, A299765, A328365.

Sequence in context: A121208 A331914 A324935 * A207674 A162722 A123345

Adjacent sequences: A328366 A328367 A328368 * A328370 A328371 A328372

Keyword

nonn

Author

Omar E. Pol, Nov 04 2019

Status

approved