A072499 - OEIS

%I #27 Dec 19 2023 13:41:43

%S 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,

%T 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,

%U 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

%N Product of divisors of n which are <= n^(1/2).

%C 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

%C Row products of the table in A161906. - _Reinhard Zumkeller_, Mar 08 2013

%C It appears that the fixed points belong to 3 categories: p^6 (A030516), p^3*q, or p*q*r. - _Michel Marcus_, May 16 2014

%H Reinhard Zumkeller, <a href="/A072499/b072499.txt">Table of n, a(n) for n = 1..10000</a>

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

%t a[n_] := Times @@ Select[Divisors[n], #^2 <= n &]; Array[a, 100] (* _Amiram Eldar_, Jul 31 2022 *)

%o (Haskell)

%o a072499 = product . a161906_row  -- _Reinhard Zumkeller_, Mar 08 2013

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

%o (Python)

%o from math import prod

%o from itertools import takewhile

%o from sympy import divisors

%o def A072499(n): return prod(takewhile(lambda x:x**2<=n,divisors(n))) # _Chai Wah Wu_, Dec 19 2023

%Y Cf. A072500, A072501, A161906.

%Y Cf. A072504, A066839.

%K nonn

%O 1,4

%A _Amarnath Murthy_, Jul 20 2002

%E More terms from _Sascha Kurz_, Feb 02 2003