A089189 Primes p such that p-1 is cubefree.
2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 79, 83, 101, 103, 107, 127, 131, 139, 149, 151, 157, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 239, 263, 269, 277, 283, 293, 307, 311, 317, 331, 347, 349, 359, 367, 373, 383
Offset: 1
Examples
43 is included because 43-1 = 2*3*7. 41 is omitted because 41-1 = 2^3*5. 97 is omitted because 96 = 2^5*3 since higher powers are also tested for exclusion.
Links
- Reinhard Zumkeller and Vincenzo Librandi, Table of n, a(n) for n = 1..10000
- Leon Mirsky, The number of representations of an integer as the sum of a prime and a k-free integer, American Mathematial Monthly 56:1 (1949), pp. 17-19.
Programs
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Haskell
a097375 n = a097375_list !! (n-1) a097375_list = filter ((== 1) . a212793 . (subtract 1)) a000040_list -- Reinhard Zumkeller, May 27 2012
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Maple
filter:= p -> isprime(p) and max(seq(t[2],t=ifactors(p-1)[2]))<=2: select(filter, [2,seq(2*i+1,i=1..1000)]); # Robert Israel, Sep 11 2014
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Mathematica
f[n_]:=Module[{a=m=0},Do[If[FactorInteger[n][[m,2]]>2,a=1],{m,Length[FactorInteger[n]]}];a]; lst={};Do[p=Prime[n];If[f[p-1]==0,AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 15 2009 *) Select[Prime[Range[100]],Max[Transpose[FactorInteger[#-1]][[2]]]<3&] (* Harvey P. Dale, Feb 05 2012 *) -
PARI
lista(nn) = forprime(p=2, nn, f = factor(p-1)[,2]; if ((#f == 0) || vecmax(f) < 3, print1(p, ", "));) \\ Michel Marcus, Sep 11 2014
Formula
A212793(a(n) - 1) = 1. - Reinhard Zumkeller, May 27 2012
Extensions
Corrected and extended by Harvey P. Dale, Feb 05 2012
Comments