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 A301987 Heinz numbers of integer partitions whose product is equal to their sum. 59
 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 84, 89, 97, 101, 103, 107, 108, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 200, 211, 223, 227, 229, 233, 239, 241, 251 (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 Alois P. Heinz, Table of n, a(n) for n = 1..10000 EXAMPLE Sequence of reversed integer partitions begins: (1), (2), (3), (4), (2 2), (5), (6), (7), (8), (9), (10), (1 2 3), (11), (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (1 1 2 4), (24), (25), (26), (27), (28), (1 1 2 2 2), (29), (30). MAPLE q:= n-> (l-> mul(i, i=l)=add(i, i=l))(map(i-> numtheory[pi](i[1])\$i[2], ifactors(n)[2])): select(q, [\$1..300])[]; # Alois P. Heinz, Mar 27 2019 MATHEMATICA primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[300], Total[primeMS[#]]===Times@@primeMS[#]&] CROSSREFS Cf. A001055, A002865, A003963, A056239, A276024, A284640, A296150, A299701, A301957, A301988. Sequence in context: A136327 A095415 A326149 * A353393 A316857 A318589 Adjacent sequences: A301984 A301985 A301986 * A301988 A301989 A301990 KEYWORD nonn AUTHOR Gus Wiseman, Mar 30 2018 STATUS approved

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Last modified December 5 16:58 EST 2022. Contains 358588 sequences. (Running on oeis4.)