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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. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 6 15:34 EDT 2020. Contains 336252 sequences. (Running on oeis4.)