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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 Table of n, a(n) for n=1..47. 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. Cf. A001222, A047993, A056239, A061395, A067538, A112798, A316413, A326836, A326843, A326847, A326848, A326851. Sequence in context: A277980 A241025 A326309 * A098996 A130862 A070756 Adjacent sequences: A326835 A326836 A326837 * A326839 A326840 A326841 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.)