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

1,3

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

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

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 *)

Prog

(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));

Crossrefs

A left inverse of A334747.

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

Sequence in context: A321908 A130728 A276085 * A324122 A324349 A092384

Adjacent sequences: A334867 A334868 A334869 * A334871 A334872 A334873

Keyword

nonn

Author

Antti Karttunen, Jun 08 2020

Status

approved