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A316151
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Heinz numbers of strict integer partitions of prime numbers into prime parts.
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1
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3, 5, 11, 15, 17, 31, 33, 41, 59, 67, 83, 93, 109, 127, 157, 177, 179, 191, 211, 241, 277, 283, 327, 331, 353, 367, 401, 431, 461, 509, 537, 547, 563, 587, 599, 617, 709, 739, 773, 797, 831, 859, 877, 919, 967, 991, 1031, 1059, 1063, 1087, 1153, 1171, 1201
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OFFSET
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1,1
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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).
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LINKS
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Table of n, a(n) for n=1..53.
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EXAMPLE
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Sequence of strict integer partitions of prime numbers into prime parts, preceded by their Heinz numbers, begins:
3: (2)
5: (3)
11: (5)
15: (3,2)
17: (7)
31: (11)
33: (5,2)
41: (13)
59: (17)
67: (19)
83: (23)
93: (11,2)
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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[100], And[SquareFreeQ[#], PrimeQ[Total[primeMS[#]]], And@@PrimeQ/@primeMS[#]]&]
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CROSSREFS
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Cf. A000586, A000607, A038499, A056239, A056768, A064688, A070215, A085755, A302590, A316092.
Sequence in context: A153798 A316092 A302590 * A265121 A281575 A105772
Adjacent sequences: A316148 A316149 A316150 * A316152 A316153 A316154
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Jun 25 2018
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STATUS
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approved
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