login
A048945
Numbers whose product of divisors is a fourth power.
4
1, 24, 30, 40, 42, 54, 56, 66, 70, 78, 88, 102, 104, 105, 110, 114, 120, 128, 130, 135, 136, 138, 152, 154, 165, 168, 170, 174, 182, 184, 186, 189, 190, 195, 210, 216, 222, 230, 231, 232, 238, 246, 248, 250, 255, 256, 258, 264, 266, 270, 273, 280, 282, 285
OFFSET
1,2
COMMENTS
Different from sequence of numbers which are the cube root of the product of their proper divisors. Compare A111398.
REFERENCES
Amarnath Murthy, Generalization of Partition function, Introducing Smarandache Factor partitions, Smarandache Notions Journal, Vol. 11, 1-2-3, Spring 2000.
Amarnath Murthy, A note on Smarandache Divisor Sequence, Introducing Smarandache Factor partitions, Smarandache Notions Journal, Vol. 11, 1-2-3, Spring 2000.
Amarnath Murthy, Some more ideas on Smarandache Factor Partitions, Smarandache Notions Journal, Vol. 11, 1-2-3, Spring 2000.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Divisor Product
MAPLE
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:
MATHEMATICA
Select[Range[300], IntegerQ[(Times @@ Divisors[#])^(1/4)] &] (* Jean-François Alcover, Nov 05 2012 *)
PROG
(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
CROSSREFS
Sequence in context: A129656 A372299 A334974 * A111398 A030626 A302571
KEYWORD
nonn
STATUS
approved