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A316428
Heinz numbers of integer partitions such that every part is divisible by the number of parts.
26
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).
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[#]]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 02 2018
STATUS
approved