A334870 If n is a square, a(n) = A000196(n), and for nonsquare n, let p be the smallest prime dividing the squarefree part of n. Divide n by p and multiply by the product of all smaller primes.

1, 1, 2, 2, 6, 3, 30, 4, 3, 5, 210, 8, 2310, 7, 10, 4, 30030, 9, 510510, 24, 14, 11, 9699690, 12, 5, 13, 18, 120, 223092870, 15, 6469693230, 16, 22, 17, 42, 6, 200560490130, 19, 26, 20, 7420738134810, 21, 304250263527210, 840, 54, 23, 13082761331670030, 32, 7, 25, 34, 9240, 614889782588491410, 27, 66, 28, 38, 29

Offset: 1

Author

Antti Karttunen, Jun 08 2020

Keywords

• nonn

Comments

Each natural numbers occurs exactly twice in this sequence.

In binary trees like A334860 and A334866, for n > 2, a(n) gives the parent node of node n.

For nonsquare numbers, n, with squarefree part A019565(k) and square part m, a(n) is the number with squarefree part A019565(k-1) and square part m. - Peter Munn, Jul 14 2020

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024

Crossrefs

A left inverse of A334747.

Cf. A000196, A019565, A225546, A252463, A334860, A334866, A334868, A334869, A334871, A334872.

Programs

Mathematica

Array[If[IntegerQ[#2], #2, #1/#2*Product[Prime@i, {i, PrimePi@#2 - 1}] & @@ {#1, FactorInteger[#2 /. (c_ : 1)*a_^(b_ : 0) :> (c*a^b)^2][[1, 1]]}] & @@ {#, Sqrt[#]} &, 58] (* Michael De Vlieger, Jun 26 2020 *)

PARI

A334870(n) = if(issquare(n),sqrtint(n),my(c=core(n), m=n); forprime(p=2, , if(!(c % p), m/=p; break, m*=p)); (m));

Formula

a(A334747(n)) = n.

a(A000040(n)) = A002110(n-1).

a(n^2) = n.

a(n) = A225546(A252463(A225546(n))). - Peter Munn, Jun 08 2020