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A330225 Position of first appearance of n in A290103 = LCM of prime indices. 2

%I #9 Mar 28 2020 13:08:37

%S 1,3,5,7,11,13,17,19,23,29,31,35,41,43,47,53,59,61,67,71,73,79,83,89,

%T 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,

%U 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271

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

%C Appears to be the prime numbers (A000040) with 2 replaced by 1 and 37 replaced by 35.

%C 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.

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t q=Table[If[n==1,1,LCM@@primeMS[n]],{n,100}];

%t Table[Position[q,i][[1,1]],{i,First[Split[Union[q],#1+1==#2&]]}]

%Y The version for product instead of lcm is A318871

%Y The version for standard compositions is A333225.

%Y The version for binary indices is A333492.

%Y Let q(k) be the prime indices of k:

%Y - The product of q(k) is A003963(k).

%Y - The sum of q(k) is A056239(k).

%Y - The terms of q(k) are row k of A112798.

%Y - The GCD of q(k) is A289508(k).

%Y - The LCM of q(k) is A290103(k).

%Y - The LCM of q(k) + 1 is A328219(k).

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Mar 26 2020

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Last modified April 24 20:08 EDT 2024. Contains 371963 sequences. (Running on oeis4.)