A048945 Numbers whose product of divisors is a fourth power.

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

Author

Eric W. Weisstein

Keywords

• nonn

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

Crossrefs

Cf. A111398, A111399.

Programs

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 *)

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