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A175670 Composite numbers n such that p^2 * (p - 1) divides 2(n - p) for every prime p dividing n. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A261650 A178731 A071072 * A194374 A061085 A007883

Adjacent sequences:  A175667 A175668 A175669 * A175671 A175672 A175673

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Dec 20 2011

STATUS

approved

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Last modified March 25 09:41 EDT 2017. Contains 284060 sequences.