

A290103


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


81



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, 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, 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
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OFFSET

1,3


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences related to lcm's
Index entries for sequences computed from indices in prime factorization


FORMULA

a(1) = 1; for n > 1, a(n) = lcm(A055396(n), a(A028234(n)).
Other identities. For all n >= 1:
a(A007947(n)) = a(n).
a(A181819(n)) = A072411(n).


EXAMPLE

Here primepi (A000720) gives the index of its prime argument:
n = 14 = 2 * 7, thus a(14) = lcm(primepi(2), primepi(7)) = lcm(1,4) = 4.
n = 21 = 3 * 7, thus a(21) = lcm(primepi(3), primepi(7)) = lcm(2,4) = 4.


MATHEMATICA

Table[Apply[LCM, PrimePi[FactorInteger[n][[All, 1]] ]] + Boole[n == 1], {n, 105}] (* Michael De Vlieger, Aug 14 2017 *)


PROG

(Scheme) (define (A290103 n) (if (= 1 n) n (lcm (A055396 n) (A290103 (A028234 n))))) ;; Antti Karttunen, Aug 13 2017
(PARI) a(n)=if(n>1, lcm(apply(primepi, factor(n)[, 1])), 1) \\ Charles R Greathouse IV, Nov 11 2021


CROSSREFS

Cf. A000040, A000720, A003963, A007947, A156061, A290104, A290105.
Cf. also A072411, A181819.
Sequence in context: A324729 A253558 A061395 * A156061 A225395 A295877
Adjacent sequences: A290100 A290101 A290102 * A290104 A290105 A290106


KEYWORD

nonn


AUTHOR

Antti Karttunen, Aug 13 2017


STATUS

approved



