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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 Amiram Eldar, Table of n, a(n) for n = 1..1000 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 Cf. A244428, A064121, A229972, A194948. Sequence in context: A048540 A189497 A219712 * A005931 A027793 A244945 Adjacent sequences: A244426 A244427 A244428 * A244430 A244431 A244432 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.)