

A244429


Nonprimes n such that the sum of proper divisors of n and the product of proper divisors of n are both perfect cubes.


1



1, 56, 568, 1001, 1431, 3344, 10688, 17619, 24099, 37432, 40797, 46096, 50571, 52687, 55581, 62375, 75221, 88863, 97273, 98752, 111224, 134672, 235495, 247033, 251403, 266176, 269072, 271099, 275077, 299576, 320489, 333888, 364067, 372331, 407319, 534413, 561008, 614465, 646691
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OFFSET

1,2


COMMENTS

Primes trivially satisfy this property and are therefore not included in this sequence.


LINKS



EXAMPLE

The proper divisors of 56 are {1, 2, 4, 7, 8, 14, 28}. 1*2*4*7*8*14*28 = 175616 = 56^3. 1+2+4+7+8+14+28 = 64 = 4^3. Since both the product of proper divisors and the sum of proper divisors are cubes, 56 is a member of this sequence.


PROG

(PARI) for(n=1, 10^7, d=divisors(n); s=sum(i=1, #d1, d[i]); p=prod(j=1, #d1, d[j]); if((p!=1s!=1), if(ispower(s, 3)&&ispower(p, 3), print1(n, ", "))))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



