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A316151 Heinz numbers of strict integer partitions of prime numbers into prime parts. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

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)

MATHEMATICA

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[#]]&]

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 25 2018

STATUS

approved

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Last modified February 5 10:17 EST 2023. Contains 360084 sequences. (Running on oeis4.)