A111399 -id:A111399 - cp's OEIS frontend

A111398 Numbers which are the cube roots of the product of their proper divisors.

1, 24, 30, 40, 42, 54, 56, 66, 70, 78, 88, 102, 104, 105, 110, 114, 128, 130, 135, 136, 138, 152, 154, 165, 170, 174, 182, 184, 186, 189, 190, 195, 222, 230, 231, 232, 238, 246, 248, 250, 255, 258, 266, 273, 282, 285, 286, 290, 296, 297

Offset: 1

Ant King, Nov 11 2005

nonn

This sequence is actually the sequence of 4-multiplicatively perfect numbers all of whose elements (>1) have prime signature {7}, {1,3} or {1,1,1}.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A048945, A111399. Essentially the same as A030626.

Cf. A030626, A007956.

Select[Range[300],Surd[Times@@Most[Divisors[#]],3]==#&] (* Harvey P. Dale, Nov 16 2015 *)

isok(n) = {prd = 1; fordiv(n, d, prd = prd*d); prd == n^4;} \\ Michel Marcus, Oct 04 2013

1 together with numbers with 8 divisors. - Vladeta Jovovic, Nov 12 2005

More terms from Michel Marcus, Oct 04 2013

A048945 Numbers whose product of divisors is a fourth power.

Original entry on oeis.org

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

Eric W. Weisstein

nonn

Different from sequence of numbers which are the cube root of the product of their proper divisors. Compare A111398.

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.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Divisor Product

Cf. A111398, A111399.

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:

Select[Range[300], IntegerQ[(Times @@ Divisors[#])^(1/4)] &] (* Jean-François Alcover, Nov 05 2012 *)

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

cp's OEIS Frontend

A111398 Numbers which are the cube roots of the product of their proper divisors.

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