OFFSET
1,1
COMMENTS
Also Heinz numbers of a type of sum-full partitions not allowing re-used parts, counted by A237113.
All multiples of terms are terms. - Robert Israel, Aug 30 2023
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
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 i-1 do
if member(F[i]+F[j], F) then return true fi
od od;
false
end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 30 2023
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 29 2023
STATUS
approved