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A072499 Product of divisors of n which are <= n^(1/2). 8
1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 6, 1, 2, 3, 8, 1, 6, 1, 8, 3, 2, 1, 24, 5, 2, 3, 8, 1, 30, 1, 8, 3, 2, 5, 144, 1, 2, 3, 40, 1, 36, 1, 8, 15, 2, 1, 144, 7, 10, 3, 8, 1, 36, 5, 56, 3, 2, 1, 720, 1, 2, 21, 64, 5, 36, 1, 8, 3, 70, 1, 1152, 1, 2, 15, 8, 7, 36, 1, 320, 27, 2, 1, 1008, 5, 2, 3, 64, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(1) = 1 and a(24) = 24. For each pair of primes p,q such that p < q < p^2, if n = p^3*q, then a(n) = n. There are others as well; e.g. a(40)=40. - Don Reble, Aug 02 2002

Row products of the table in A161906. - Reinhard Zumkeller, Mar 08 2013

It appears that numbers such that a(n)=n belong to 3 categories: p^6 (A030516), p^3*q, or p*q*r. - Michel Marcus, May 16 2014

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

a(20) = 8. The divisors of 20 are 1,2,4,5,10 and 20. a(20) = 1*2*4 = 8.

PROG

(Haskell)

a072499 = product . a161906_row  -- Reinhard Zumkeller, Mar 08 2013

(PARI) a(n) = my(d = divisors(n)); prod(i=1, #d, if (d[i]^2 <= n, d[i], 1)); \\ Michel Marcus, May 16 2014

CROSSREFS

Cf. A072500, A072501.

Cf. A072504, A066839.

Sequence in context: A070966 A219254 A072504 * A060272 A209315 A174713

Adjacent sequences:  A072496 A072497 A072498 * A072500 A072501 A072502

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jul 20 2002

EXTENSIONS

More terms from Sascha Kurz, Feb 02 2003

STATUS

approved

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)