A301987 Heinz numbers of integer partitions whose product is equal to their sum.

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

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