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 A325327 Heinz numbers of multiples of triangular partitions, or finite arithmetic progressions with offset 0. 14
 1, 2, 3, 5, 6, 7, 11, 13, 17, 19, 21, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 61, 65, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 133, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 210, 211, 223, 227, 229, 233, 239 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). Also numbers of the form Product_{k = 1..b} prime(k * c) for some b >= 0 and c > 0. The enumeration of these partitions by sum is given by A007862. LINKS EXAMPLE The sequence of terms together with their prime indices begins:     1: {}     2: {1}     3: {2}     5: {3}     6: {1,2}     7: {4}    11: {5}    13: {6}    17: {7}    19: {8}    21: {2,4}    23: {9}    29: {10}    30: {1,2,3}    31: {11}    37: {12}    41: {13}    43: {14}    47: {15}    53: {16} MATHEMATICA primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]; Select[Range[100], SameQ@@Differences[Append[primeptn[#], 0]]&] CROSSREFS Cf. A000961, A007294, A007862, A049988, A056239, A112798, A130091, A289509, A307824, A325328, A325367, A325390, A325407. Sequence in context: A283599 A096530 A299157 * A003174 A238463 A166070 Adjacent sequences:  A325324 A325325 A325326 * A325328 A325329 A325330 KEYWORD nonn AUTHOR Gus Wiseman, Apr 23 2019 STATUS approved

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Last modified December 12 01:57 EST 2019. Contains 329948 sequences. (Running on oeis4.)