A330225 - OEIS

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A330225

Position of first appearance of n in A290103 = LCM of prime indices.

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

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.

LINKS

Table of n, a(n) for n=1..58.

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).

Cf. A000837, A074761, A074971, A076078, A285572, A289509, A290104, A319333, A324837, A328451, A331579, A333226.

Sequence in context: A210494 A338483 A318871 * A275938 A093893 A056912

Adjacent sequences: A330222 A330223 A330224 * A330226 A330227 A330228

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 26 2020

STATUS

approved