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

1,2

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

Cf. A111398, A111399.

Sequence in context: A109797 A129656 A334974 * A111398 A030626 A302571

Adjacent sequences: A048942 A048943 A048944 * A048946 A048947 A048948

Keyword

nonn

Author

Eric W. Weisstein

Status

approved