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A318606 Numbers of the form p^k-k for some prime, p, and integer k >= 0. 1

%I #28 Sep 14 2019 06:39:15

%S 1,2,4,5,6,7,10,12,16,18,22,23,24,27,28,30,36,40,42,46,47,52,58,60,66,

%T 70,72,77,78,82,88,96,100,102,106,108,112,119,121,122,126,130,136,138,

%U 148,150,156,162,166,167,172,178,180,190,192,196,198,210,222,226,228,232,238,240,248,250,256,262

%N Numbers of the form p^k-k for some prime, p, and integer k >= 0.

%H Jud McCranie, <a href="/A318606/b318606.txt">Table of n, a(n) for n = 1..5000</a>

%H S. P. Hurd and J. S. McCranie, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Hurd/hurd1.html">Integers that are Sums of Uniform Powers of all their Prime Factors: the sequence A068916</a>, J. of Int. Seq., vol 22 (2019), article 19.3.4.

%e 2^7-7=121, so 121 is in the sequence.

%t With[{nn = 265}, Union@ Flatten@ Table[p^k - k, {p, Prime@ Range@ PrimePi@ nn}, {k, Log[p, nn]}]] (* _Michael De Vlieger_, Jul 16 2019 *)

%Y Cf. A000040, A057897, A068916, A269769.

%K nonn

%O 1,2

%A _Jud McCranie_, Aug 29 2018

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Last modified April 25 06:42 EDT 2024. Contains 371964 sequences. (Running on oeis4.)