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

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

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: A364192 A253558 A061395 * A156061 A225395 A295877

Adjacent sequences: A290100 A290101 A290102 * A290104 A290105 A290106

Keyword

nonn

Author

Antti Karttunen, Aug 13 2017

Status

approved