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

Offset: 1

Author

Gus Wiseman, Mar 26 2020

Keywords

• nonn

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.

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.

Programs

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&]]}]