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
Offset: 1
Keywords
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1000
Programs
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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,", "))))
Comments