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A325407
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Nonprime Heinz numbers of multiples of triangular partitions, or of finite arithmetic progressions with offset 0.
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11
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1, 6, 21, 30, 65, 133, 210, 273, 319, 481, 731, 1007, 1403, 1495, 2059, 2310, 2449, 3293, 4141, 4601, 4921, 5187, 5311, 6943, 8201, 9211, 10921, 12283, 13213, 14993, 15247, 16517, 19847, 22213, 24139, 25853, 28141, 29341, 29539, 30030, 31753, 37211, 40741
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OFFSET
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1,2
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COMMENTS
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The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are numbers of the form Product_{k = 1...b} prime(k * c) for some b > 1 and c > 0.
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LINKS
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Table of n, a(n) for n=1..43.
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EXAMPLE
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The sequence of terms together with their prime indices begins:
1: {}
6: {1,2}
21: {2,4}
30: {1,2,3}
65: {3,6}
133: {4,8}
210: {1,2,3,4}
273: {2,4,6}
319: {5,10}
481: {6,12}
731: {7,14}
1007: {8,16}
1403: {9,18}
1495: {3,6,9}
2059: {10,20}
2310: {1,2,3,4,5}
2449: {11,22}
3293: {12,24}
4141: {13,26}
4601: {14,28}
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[10000], !PrimeQ[#]&&SameQ@@Differences[Prepend[primeMS[#], 0]]&]
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CROSSREFS
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Cf. A007294, A007862, A049988, A056239, A112798, A325327, A325328, A325355, A325359, A325367, A325390.
Sequence in context: A347875 A287165 A280296 * A239920 A173622 A302868
Adjacent sequences: A325404 A325405 A325406 * A325408 A325409 A325410
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, May 03 2019
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STATUS
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approved
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