A244429 - OEIS

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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, 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.

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