A301987 - OEIS

%I #10 Mar 27 2019 12:33:18

%S 2,3,5,7,9,11,13,17,19,23,29,30,31,37,41,43,47,53,59,61,67,71,73,79,

%T 83,84,89,97,101,103,107,108,109,113,127,131,137,139,149,151,157,163,

%U 167,173,179,181,191,193,197,199,200,211,223,227,229,233,239,241,251

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

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

%H Alois P. Heinz, <a href="/A301987/b301987.txt">Table of n, a(n) for n = 1..10000</a>

%e 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).

%p q:= n-> (l-> mul(i, i=l)=add(i, i=l))(map(i->

%p     numtheory[pi](i[1])$i[2], ifactors(n)[2])):

%p select(q, [$1..300])[];  # _Alois P. Heinz_, Mar 27 2019

%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[300],Total[primeMS[#]]===Times@@primeMS[#]&]

%Y Cf. A001055, A002865, A003963, A056239, A276024, A284640, A296150, A299701, A301957, A301988.

%K nonn

%O 1,1

%A _Gus Wiseman_, Mar 30 2018