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A328677
Numbers whose distinct prime indices are relatively prime and pairwise indivisible.
9
2, 4, 8, 15, 16, 32, 33, 35, 45, 51, 55, 64, 69, 75, 77, 85, 93, 95, 99, 119, 123, 128, 135, 141, 143, 145, 153, 155, 161, 165, 175, 177, 187, 201, 205, 207, 209, 215, 217, 219, 221, 225, 245, 249, 253, 255, 256, 265, 275, 279, 287, 291, 295, 297, 309, 323
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. Stable numbers are listed in A316476.
FORMULA
Intersection of A316476 and A289509.
EXAMPLE
The sequence of terms together with their prime indices begins:
2: {1}
4: {1,1}
8: {1,1,1}
15: {2,3}
16: {1,1,1,1}
32: {1,1,1,1,1}
33: {2,5}
35: {3,4}
45: {2,2,3}
51: {2,7}
55: {3,5}
64: {1,1,1,1,1,1}
69: {2,9}
75: {2,3,3}
77: {4,5}
85: {3,7}
93: {2,11}
95: {3,8}
99: {2,2,5}
119: {4,7}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Select[Range[100], GCD@@primeMS[#]==1&&stableQ[primeMS[#], Divisible]&]
CROSSREFS
These are the Heinz numbers of the partitions counted by A328676.
Numbers whose prime indices are relatively prime are A289509.
Partitions whose distinct parts are pairwise indivisible are A305148.
The version for binary indices (instead of prime indices) is A328671.
Sequence in context: A354192 A076351 A140117 * A039743 A070008 A033623
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 30 2019
STATUS
approved