A175670 Composite numbers n such that p^2 * (p - 1) divides 2(n - p) for every prime p dividing n.

4, 8, 12, 16, 32, 48, 64, 128, 192, 256, 448, 512, 768, 1024, 2048, 3072, 4096, 8192, 12288, 16384, 28672, 32768, 49152, 65536, 131072, 196608, 262144, 524288, 786432, 1048576, 1835008, 2097152, 3145728, 4194304, 4980736, 8388608, 11534336, 12582912

Offset

1,1

Comments

On the other hand, no composite numbers are known such that p^2 * (p-1) divides (n-p) for every prime p dividing n.

Links

Table of n, a(n) for n=1..38.

Mathematica

hh[n_] := Module[{aux = FactorInteger[n]}, Union@Table[IntegerQ[2 (n - aux[[i, 1]])/(aux[[i, 1]]^2 * (aux[[i, 1]] - 1))], {i, 1, Length[aux]}] == {True}]; Select[1+Range[50000], !PrimeQ[#] && hh[#] &]

Prog

(PARI) p=3; forprime(q=5, 1e7, for(n=p+1, q-1, f=factor(n)[, 1]; for(i=1, #f, if(2*(n-f[i])%(f[i]^2*(f[i]-1)), next(2))); print1(n", ")); p=q) \\ Charles R Greathouse IV, Dec 21 2011

Crossrefs

Sequence in context: A178731 A334386 A071072 * A355031 A194374 A061085

Adjacent sequences: A175667 A175668 A175669 * A175671 A175672 A175673

Keyword

nonn

Author

José María Grau Ribas, Dec 20 2011

Status

approved