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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
OFFSET
1,2
COMMENTS
Primes trivially satisfy this property and are therefore not included in this sequence.
These numbers are in the intersection of A194948 and A229972.
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, #d-1, d[i]); p=prod(j=1, #d-1, d[j]); if((p!=1||s!=1), if(ispower(s, 3)&&ispower(p, 3), print1(n, ", "))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Derek Orr, Jun 27 2014
STATUS
approved