cp's OEIS Frontend

A114871 Numbers of the form (p-1)p^k (where p is a prime and k>=0) in ascending order.

%I A114871 #13 Feb 10 2021 19:34:28
%S A114871 1,2,4,6,8,10,12,16,18,20,22,28,30,32,36,40,42,46,52,54,58,60,64,66,
%T A114871 70,72,78,82,88,96,100,102,106,108,110,112,126,128,130,136,138,148,
%U A114871 150,156,162,166,172,178,180,190,192,196,198,210,222,226,228,232,238,240,250
%N A114871 Numbers of the form (p-1)p^k (where p is a prime and k>=0) in ascending order.
%C A114871 These numbers play a crucial role in inverting Euler's totient function.
%H A114871 Robert Israel, <a href="/A114871/b114871.txt">Table of n, a(n) for n = 1..10000</a>
%H A114871 S. Contini, E. Croot, I. E. Shparlinski, <a href="https://arxiv.org/abs/math/0404116">Complexity of Inverting the Euler Function</a>, arXiv:math/0404116 [math.NT], 2004.
%e A114871 18 is an element of the sequence because 18=(3-1)3^2 and 3 is a prime.
%p A114871 N:= 1000: # for terms <= N
%p A114871 S:= {}: R:= NULL:
%p A114871 p:= 1:
%p A114871 while p <= N do
%p A114871   p:= nextprime(p);
%p A114871   S:= S union {seq((p-1)*p^k, k = 0..ilog[p](N/(p-1)))};
%p A114871   R:= R, seq((p-1)*p^k, k = 0..ilog[p](N/(p-1)))
%p A114871 od:
%p A114871 sort(convert(S,list)); # _Robert Israel_, Feb 10 2021
%t A114871 Take[Union@ Flatten@ Table[(Prime[n] - 1)Prime[n]^k, {n, 60}, {k, 0, 7}], 61] (* _Robert G. Wilson v_, Jan 05 2006 *)
%K A114871 nonn
%O A114871 1,2
%A A114871 _Franz Vrabec_, Jan 03 2006
%E A114871 More terms from _Robert G. Wilson v_, Jan 05 2006