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A328677
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Numbers whose distinct prime indices are relatively prime and pairwise indivisible.
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9
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..56.
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FORMULA
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Intersection of A316476 and A289509.
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EXAMPLE
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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}
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MATHEMATICA
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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]&]
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CROSSREFS
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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.
Cf. A000837, A056239, A112798, A285573, A289508, A303362, A304713, A327393, A328460.
Sequence in context: A275474 A076351 A140117 * A039743 A070008 A033623
Adjacent sequences: A328674 A328675 A328676 * A328678 A328679 A328680
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Oct 30 2019
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STATUS
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approved
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