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A164517 Primes of the form 1+A162143(k). 4
4357, 12101, 16901, 28901, 52901, 164837, 184901, 220901, 224677, 417317, 427717, 682277, 792101, 820837, 894917, 972197, 1020101, 1110917, 1136357, 1144901, 1223237, 1313317, 1552517, 1887877, 1943237, 1976837, 2056357, 2464901 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes p such that p-1 equals the square of a product of three distinct primes.

Primes of the similar form A162143(k)-1 do not exist, because A162143 are squares

which allows for the obvious factorization A162143(k)-1 = (A007304(k)+1)*(A007304(k)-1).

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

For p=4357=a(1), p=14356=2^2*3^2*11^2. For p=12101, p=1=12100=2^2*5^2*11^2.

MATHEMATICA

f[n_]:=FactorInteger[n][[1, 2]]==2&&Length[FactorInteger[n]]==3&&FactorInteger[n][[2, 2]]==2&&FactorInteger[n][[3, 2]]==2; lst={}; Do[p=Prime[n]; If[f[p-1], AppendTo[lst, p]], {n, 2, 9!}]; lst

CROSSREFS

Sequence in context: A285040 A203928 A176111 * A125825 A031564 A217345

Adjacent sequences:  A164514 A164515 A164516 * A164518 A164519 A164520

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Aug 14 2009

EXTENSIONS

Edited by R. J. Mathar, Aug 18 2009

STATUS

approved

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Last modified October 16 10:43 EDT 2018. Contains 316262 sequences. (Running on oeis4.)