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A326838 Heinz numbers of non-constant integer partitions whose length and maximum both divide their sum. 4
30, 84, 264, 273, 286, 325, 351, 364, 390, 441, 490, 525, 624, 756, 784, 810, 840, 874, 900, 988, 1000, 1173, 1197, 1254, 1330, 1425, 1495, 1632, 1771, 2079, 2156, 2178, 2204, 2294, 2310, 2420, 2475, 2750, 2958, 3219, 3393, 3648, 3726, 3770, 3864, 3944, 4042 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
The enumeration of these partitions by sum is given by A326852.
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
30: {1,2,3}
84: {1,1,2,4}
264: {1,1,1,2,5}
273: {2,4,6}
286: {1,5,6}
325: {3,3,6}
351: {2,2,2,6}
364: {1,1,4,6}
390: {1,2,3,6}
441: {2,2,4,4}
490: {1,3,4,4}
525: {2,3,3,4}
624: {1,1,1,1,2,6}
756: {1,1,2,2,2,4}
784: {1,1,1,1,4,4}
810: {1,2,2,2,2,3}
840: {1,1,1,2,3,4}
874: {1,8,9}
900: {1,1,2,2,3,3}
988: {1,1,6,8}
MATHEMATICA
Select[Range[1000], With[{y=Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]}, !SameQ@@y&&Divisible[Total[y], Max[y]]&&Divisible[Total[y], Length[y]]]&]
CROSSREFS
The possibly constant case is A326837.
Sequence in context: A277980 A241025 A326309 * A098996 A130862 A070756
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2019
STATUS
approved

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Last modified April 24 06:14 EDT 2024. Contains 371918 sequences. (Running on oeis4.)