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

Author

Omar E. Pol, Nov 04 2019

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Crossrefs

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

Programs

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 *)