|
%I #16 Jun 18 2021 18:58:58
%S 1,24,30,40,42,54,56,66,70,78,88,102,104,105,110,114,120,128,130,135,
%T 136,138,152,154,165,168,170,174,182,184,186,189,190,195,210,216,222,
%U 230,231,232,238,246,248,250,255,256,258,264,266,270,273,280,282,285
%N Numbers whose product of divisors is a fourth power.
%C Different from sequence of numbers which are the cube root of the product of their proper divisors. Compare A111398.
%D Amarnath Murthy, Generalization of Partition function, Introducing Smarandache Factor partitions, Smarandache Notions Journal, Vol. 11, 1-2-3, Spring 2000.
%D Amarnath Murthy, A note on Smarandache Divisor Sequence, Introducing Smarandache Factor partitions, Smarandache Notions Journal, Vol. 11, 1-2-3, Spring 2000.
%D Amarnath Murthy, Some more ideas on Smarandache Factor Partitions, Smarandache Notions Journal, Vol. 11, 1-2-3, Spring 2000.
%H Charles R Greathouse IV, <a href="/A048945/b048945.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorProduct.html">Divisor Product</a>
%p for n from 2 to 1000 do it1 := sort(convert(divisors(n), list)): it2 := product(it1[j], j=1..nops(it1)-1): if it2 = n^3 then printf(`%d,`,n) fi: od:
%t Select[Range[300], IntegerQ[(Times @@ Divisors[#])^(1/4)] &] (* _Jean-François Alcover_, Nov 05 2012 *)
%o (PARI) is(n)=my(f=factor(n)[,2]); gcd(f)*prod(i=1,#f,f[i]+1)%8==0 \\ _Charles R Greathouse IV_, Sep 18 2015
%Y Cf. A111398, A111399.
%K nonn
%O 1,2
%A _Eric W. Weisstein_
|
