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A330225
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Position of first appearance of n in A290103 = LCM of prime indices.
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2
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1, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 35, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271
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OFFSET
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1,2
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COMMENTS
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Appears to be the prime numbers (A000040) with 2 replaced by 1 and 37 replaced by 35.
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.
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LINKS
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
q=Table[If[n==1, 1, LCM@@primeMS[n]], {n, 100}];
Table[Position[q, i][[1, 1]], {i, First[Split[Union[q], #1+1==#2&]]}]
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CROSSREFS
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The version for product instead of lcm is A318871
The version for standard compositions is A333225.
The version for binary indices is A333492.
Let q(k) be the prime indices of k:
- The product of q(k) is A003963(k).
- The terms of q(k) are row k of A112798.
- The LCM of q(k) + 1 is A328219(k).
Cf. A000837, A074761, A074971, A076078, A285572, A289509, A290104, A319333, A324837, A328451, A331579, A333226.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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