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 A325328 Heinz numbers of finite arithmetic progressions (integer partitions with equal differences). 20
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 67, 69, 71, 73, 74, 77, 79, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97 (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). The enumeration of these partitions by sum is given by A049988. LINKS Wikipedia, Arithmetic progression. EXAMPLE Most small numbers are in the sequence. However the sequence of non-terms together with their prime indices begins:    12: {1,1,2}    18: {1,2,2}    20: {1,1,3}    24: {1,1,1,2}    28: {1,1,4}    36: {1,1,2,2}    40: {1,1,1,3}    42: {1,2,4}    44: {1,1,5}    45: {2,2,3}    48: {1,1,1,1,2}    50: {1,3,3}    52: {1,1,6}    54: {1,2,2,2}    56: {1,1,1,4}    60: {1,1,2,3}    63: {2,2,4}    66: {1,2,5}    68: {1,1,7}    70: {1,3,4} For example, 60 is the Heinz number of (3,2,1,1), which has differences (-1,-1,0), which are not equal, so 60 does not belong to the sequence. MATHEMATICA primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]; Select[Range[100], SameQ@@Differences[primeptn[#]]&] CROSSREFS Cf. A000961, A007862, A049988, A056239, A112798, A130091, A240026, A289509, A307824, A325327, A325352, A325368, A325405, A325407. Sequence in context: A236510 A317710 A303554 * A316521 A085156 A102466 Adjacent sequences:  A325325 A325326 A325327 * A325329 A325330 A325331 KEYWORD nonn AUTHOR Gus Wiseman, Apr 23 2019 STATUS approved

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)