A367107 Numbers m not divisible by prime(bigomega(m)). Heinz numbers of integer partitions whose length is not a part (counted by A229816).

3, 4, 5, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 52, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 85

Offset: 1

Author

Gus Wiseman, Nov 21 2023

Keywords

• nonn

Comments

The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.

Crossrefs

Partitions of this type are counted by A229816.

The complement is A325761, counted by A002865.

If length is not a subset-sum: A367225, count A367213, complement A367224.

A005117 ranks strict integer partitions, counted by A000009.

A066208 ranks partitions into odd parts, also counted by A000009.

A112798 lists prime indices, reverse A296150, length A001222, sum A056239.

A237667 counts sum-free partitions, ranks A364531.

A237668 counts sum-full partitions, sum-free A364532.

Cf. A000720, A088902, A093641, A106529, A110295, A325762.

Programs

Mathematica

Select[Range[2,100],!Divisible[#,Prime[PrimeOmega[#]]]&]