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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A048540 A189497 A219712 * A005931 A027793 A244945
KEYWORD
nonn
AUTHOR
Derek Orr, Jun 27 2014
STATUS
approved

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Last modified February 23 08:25 EST 2024. Contains 370269 sequences. (Running on oeis4.)