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A113839 Powerful numbers (definition 1) sandwiched between twin primes. 8
4, 72, 108, 432, 1152, 2592, 3528, 9000, 18252, 20808, 21600, 34848, 49392, 69192, 83232, 103968, 139968, 180000, 197568, 264600, 345600, 362952, 438048, 444528, 472392, 649800, 734472, 808992, 995328, 1143072, 1190700, 1254528, 1529388, 1685448, 1960200, 2056752 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Here we are considering powerful numbers defined in A001694.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Donovan Johnson)
Eric Weisstein's World of Mathematics, Powerful Number.
EXAMPLE
72 = 2^3*3^2 is powerful and 71 and 73 are twin primes, so 72 is in the sequence.
MATHEMATICA
pwfQ[n_] := n == 1 || Min[Transpose[FactorInteger@n][[2]]] > 1; lst={}; Do[If[PrimeQ[n-1] && PrimeQ[n+1] && pwfQ[n], AppendTo[lst, n]], {n, 4, 2*10^6, 4}]; lst
PROG
(PARI) isA113839(n)=isprime(n-1)&&isprime(n+1)&&vecmax(factor(n)[, 2])>1 \\ Charles R Greathouse IV, Jun 29 2011
CROSSREFS
Intersection of A001694 and A014574.
Cf. A001097.
Sequence in context: A128062 A336253 A227248 * A077112 A203537 A095385
KEYWORD
nonn
AUTHOR
Giovanni Resta, Jan 24 2006
STATUS
approved

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)