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A364461
Positive integers such that if prime(a)*prime(b) is a divisor, prime(a+b) is not.
19
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76
OFFSET
1,2
COMMENTS
Also Heinz numbers of a type of sum-free partitions not allowing re-used parts, counted by A236912.
EXAMPLE
The prime indices of 198 are {1,2,2,5}, which is sum-free even though it is not knapsack (A299702, A299729), so 198 is in the sequence.
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 of this type are counted by A085489, with re-usable parts A007865.
Subsets not of this type are counted by A093971, w/ re-usable parts A088809.
Partitions of this type are counted by A236912.
Allowing parts to be re-used gives A364347, counted by A364345.
The complement allowing parts to be re-used is A364348, counted by A363225.
The non-binary version allowing re-used parts is counted by A364350.
The complement is A364462, counted by A237113.
The non-binary version is A364531, counted by A237667, complement A364532.
A001222 counts prime indices.
A108917 counts knapsack partitions, ranks A299702.
A112798 lists prime indices, sum A056239.
Sequence in context: A168186 A353866 A085235 * A160453 A325778 A364531
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 27 2023
STATUS
approved