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A330225
Position of first appearance of n in A290103 = LCM of prime indices.
2
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
OFFSET
1,2
COMMENTS
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.
MATHEMATICA
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&]]}]
CROSSREFS
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 sum of q(k) is A056239(k).
- The terms of q(k) are row k of A112798.
- The GCD of q(k) is A289508(k).
- The LCM of q(k) is A290103(k).
- The LCM of q(k) + 1 is A328219(k).
Sequence in context: A210494 A338483 A318871 * A275938 A093893 A056912
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2020
STATUS
approved