A049650 Compositorial numbers (A036691) + 1.

2, 5, 25, 193, 1729, 17281, 207361, 2903041, 43545601, 696729601, 12541132801, 250822656001, 5267275776001, 115880067072001, 2781121609728001, 69528040243200001, 1807729046323200001, 48808684250726400001, 1366643159020339200001

Offset: 0

Author

N. J. A. Sloane, May 05 2001

Keywords

• nonn
• easy

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..429
• Hisanori Mishima, Factorizations of many number sequences
• Hisanori Mishima, Factorizations of many number sequences

Crossrefs

Cf. A002808, A036691, A060880, A006862.

Programs

Mathematica

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 *)

Formula

a(n) = 1 + Product_{i=1..n} A002808(i). - Jonathan Vos Post, Jun 07 2008