A316428 Heinz numbers of integer partitions such that every part is divisible by the number of parts.

1, 2, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 29, 31, 37, 39, 41, 43, 47, 49, 53, 57, 59, 61, 67, 71, 73, 79, 83, 87, 89, 91, 97, 101, 103, 107, 109, 111, 113, 125, 127, 129, 131, 133, 137, 139, 149, 151, 157, 159, 163, 167, 169, 173, 179, 181, 183, 191, 193, 197

Offset

1,2

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Links

Table of n, a(n) for n=1..60.

Example

93499 is the Heinz number of (12,8,8,4) and belongs to the sequence because each part is divisible by 4.
Sequence of partitions such that every part is divisible by the number of parts begins (1), (2), (3), (4), (2,2), (5), (6), (7), (8), (4,2), (9).

Mathematica

Select[Range[200], And@@Cases[If[#==1, {}, FactorInteger[#]], {p_, k_}:>Divisible[PrimePi[p], PrimeOmega[#]]]&]

Crossrefs

Cf. A056239, A067538, A074761, A143773, A237984, A289509, A296150, A298423, A316413.

Sequence in context: A337694 A305103 A065520 * A277702 A279516 A329559

Adjacent sequences: A316425 A316426 A316427 * A316429 A316430 A316431

Keyword

nonn

Author

Gus Wiseman, Jul 02 2018

Status

approved