|
|
A367227
|
|
Numbers m whose prime indices have no nonnegative linear combination equal to bigomega(m).
|
|
24
|
|
|
3, 5, 7, 11, 13, 17, 19, 23, 25, 27, 29, 31, 35, 37, 41, 43, 47, 49, 53, 55, 59, 61, 63, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 97, 99, 101, 103, 107, 109, 113, 115, 117, 119, 121, 127, 131, 133, 137, 139, 143, 145, 147, 149, 151, 153, 155, 157, 161, 163
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
These are the Heinz numbers of the partitions counted by A367219.
|
|
LINKS
|
|
|
EXAMPLE
|
The prime indices of 24 are {1,1,1,2} with (1+1+1+1) = 4 or (1+1)+(2) = 4 or (2+2) = 4, so 24 is not in the sequence.
The terms together with their prime indices begin:
3: {2} 43: {14} 85: {3,7}
5: {3} 47: {15} 89: {24}
7: {4} 49: {4,4} 91: {4,6}
11: {5} 53: {16} 95: {3,8}
13: {6} 55: {3,5} 97: {25}
17: {7} 59: {17} 99: {2,2,5}
19: {8} 61: {18} 101: {26}
23: {9} 63: {2,2,4} 103: {27}
25: {3,3} 65: {3,6} 107: {28}
27: {2,2,2} 67: {19} 109: {29}
29: {10} 71: {20} 113: {30}
31: {11} 73: {21} 115: {3,9}
35: {3,4} 77: {4,5} 117: {2,2,6}
37: {12} 79: {22} 119: {4,7}
41: {13} 83: {23} 121: {5,5}
|
|
MATHEMATICA
|
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
combs[n_, y_]:=With[{s=Table[{k, i}, {k, y}, {i, 0, Floor[n/k]}]}, Select[Tuples[s], Total[Times@@@#]==n&]];
Select[Range[100], combs[PrimeOmega[#], Union[prix[#]]]=={}&]
|
|
CROSSREFS
|
The following sequences count and rank integer partitions and finite sets according to whether their length is a subset-sum or linear combination of the parts. The current sequence is starred.
sum-full sum-free comb-full comb-free
-------------------------------------------
A124506 appears to count combination-free subsets, differences of A326083.
Cf. A000720, A046663, A088314, A106529, A116861, A236912, A364345, A364346, A364347, A364350, A365073, A365312.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|