

A328369


Numbers without repeated parts in their partitions into consecutive parts.


1



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
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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



