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A113839 Powerful(1) numbers sandwiched between twin primes. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Here we are considering powerful numbers defined in A001694.

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..5000

Index entries for sequences related to powerful numbers

Eric Weisstein's World of Mathematics, Powerful Number

EXAMPLE

72=2^3*3^2 is powerful(1) 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

Cf. A001694, A001097.

Sequence in context: A132097 A128062 A227248 * A077112 A203537 A095385

Adjacent sequences:  A113836 A113837 A113838 * A113840 A113841 A113842

KEYWORD

nonn

AUTHOR

Giovanni Resta, Jan 24 2006

STATUS

approved

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Last modified August 25 16:43 EDT 2019. Contains 326324 sequences. (Running on oeis4.)