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A290103 a(n) = LCM of the prime indices in prime factorization of n, a(1) = 1.

%I A290103 #17 Mar 14 2025 02:35:24
%S A290103 1,1,2,1,3,2,4,1,2,3,5,2,6,4,6,1,7,2,8,3,4,5,9,2,3,6,2,4,10,6,11,1,10,
%T A290103 7,12,2,12,8,6,3,13,4,14,5,6,9,15,2,4,3,14,6,16,2,15,4,8,10,17,6,18,
%U A290103 11,4,1,6,10,19,7,18,12,20,2,21,12,6,8,20,6,22,3,2,13,23,4,21,14,10,5,24,6,12,9,22,15,24,2,25,4,10,3,26,14,27,6,12
%N A290103 a(n) = LCM of the prime indices in prime factorization of n, a(1) = 1.
%H A290103 Antti Karttunen, <a href="/A290103/b290103.txt">Table of n, a(n) for n = 1..10000</a>
%H A290103 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%H A290103 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A290103 a(1) = 1; for n > 1, a(n) = lcm(A055396(n), a(A028234(n))).
%F A290103 Other identities. For all n >= 1:
%F A290103 a(A007947(n)) = a(n).
%F A290103 a(A181819(n)) = A072411(n).
%e A290103 Here primepi (A000720) gives the index of its prime argument:
%e A290103 n = 14 = 2 * 7, thus a(14) = lcm(primepi(2), primepi(7)) = lcm(1,4) = 4.
%e A290103 n = 21 = 3 * 7, thus a(21) = lcm(primepi(3), primepi(7)) = lcm(2,4) = 4.
%t A290103 Table[Apply[LCM, PrimePi[FactorInteger[n][[All, 1]] ]] + Boole[n == 1], {n, 105}] (* _Michael De Vlieger_, Aug 14 2017 *)
%o A290103 (Scheme) (define (A290103 n) (if (= 1 n) n (lcm (A055396 n) (A290103 (A028234 n))))) ;; _Antti Karttunen_, Aug 13 2017
%o A290103 (PARI) a(n)=if(n>1, lcm(apply(primepi, factor(n)[,1])), 1) \\ _Charles R Greathouse IV_, Nov 11 2021
%Y A290103 Cf. A000040, A000720, A003963, A007947, A156061, A290104, A290105.
%Y A290103 Cf. also A072411, A181819.
%K A290103 nonn
%O A290103 1,3
%A A290103 _Antti Karttunen_, Aug 13 2017