

A364462


Positive integers having a divisor of the form prime(a)*prime(b) such that prime(a+b) is also a divisor.


19



12, 24, 30, 36, 48, 60, 63, 70, 72, 84, 90, 96, 108, 120, 126, 132, 140, 144, 150, 154, 156, 165, 168, 180, 189, 192, 204, 210, 216, 228, 240, 252, 264, 270, 273, 276, 280, 286, 288, 300, 308, 312, 315, 324, 325, 330, 336, 348, 350, 360, 372, 378, 384, 390
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OFFSET

1,1


COMMENTS

Also Heinz numbers of a type of sumfull partitions not allowing reused parts, counted by A237113.


LINKS



EXAMPLE

The terms together with their prime indices begin:
12: {1,1,2}
24: {1,1,1,2}
30: {1,2,3}
36: {1,1,2,2}
48: {1,1,1,1,2}
60: {1,1,2,3}
63: {2,2,4}
70: {1,3,4}
72: {1,1,1,2,2}
84: {1,1,2,4}
90: {1,2,2,3}
96: {1,1,1,1,1,2}
108: {1,1,2,2,2}
120: {1,1,1,2,3}
126: {1,2,2,4}
132: {1,1,2,5}
140: {1,1,3,4}
144: {1,1,1,1,2,2}


MAPLE

filter:= proc(n) local F, i, j, m;
F:= map(t > `if`(t[2]>=2, numtheory:pi(t[1])$2, numtheory:pi(t[1])), ifactors(n)[2]);
for i from 1 to nops(F)1 do for j from 1 to i1 do
if member(F[i]+F[j], F) then return true fi
od od;
false
end proc:


MATHEMATICA

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Intersection[prix[#], Total/@Subsets[prix[#], {2}]]!={}&]


CROSSREFS

Subsets not of this type are counted by A085489, w/ reusable parts A007865.
Subsets of this type are counted by A088809, with reusable parts A093971.
Partitions not of this type are counted by A236912.
Partitions of this type are counted by A237113.


KEYWORD

nonn


AUTHOR



STATUS

approved



