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A325407
Nonprime Heinz numbers of multiples of triangular partitions, or of finite arithmetic progressions with offset 0.
11
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
OFFSET
1,2
COMMENTS
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.
EXAMPLE
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}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[10000], !PrimeQ[#]&&SameQ@@Differences[Prepend[primeMS[#], 0]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 03 2019
STATUS
approved