A049650 - OEIS

%I #23 Aug 11 2024 04:24:55

%S 2,5,25,193,1729,17281,207361,2903041,43545601,696729601,12541132801,

%T 250822656001,5267275776001,115880067072001,2781121609728001,

%U 69528040243200001,1807729046323200001,48808684250726400001,1366643159020339200001

%N Compositorial numbers (A036691) + 1.

%C This is to Euclid numbers (A006862): 1 + product of first n consecutive primes, as nonprimes (A018252) are to primes (A000040). These numbers - 1, times the appropriate Euclid numbers - 1, are the factorials. Primes in this sequence include a(1) = 2, a(2) = 5, a(4) = 193, a(8) = 2903041, a(12) = 250822656001, a(17) = 1807729046323200001. - _Jonathan Vos Post_, Jun 07 2008

%H G. C. Greubel, <a href="/A049650/b049650.txt">Table of n, a(n) for n = 0..429</a>

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorizations of many number sequences</a>

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/compo_p.htm">Factorizations of many number sequences</a>

%F a(n) = 1 + Product_{i=1..n} A002808(i). - _Jonathan Vos Post_, Jun 07 2008

%t Composite[n_] := FixedPoint[n + PrimePi[#] + 1 &, n + PrimePi[n] + 1]; Table[Product[Composite[i], {i, 1, n}] + 1, {n, 0, 30}] (* _G. C. Greubel_, Dec 05 2017 *)

%Y Cf. A002808, A036691, A060880, A006862.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, May 05 2001