A182174 a(n) = prime(n)^2 - n.

3, 7, 22, 45, 116, 163, 282, 353, 520, 831, 950, 1357, 1668, 1835, 2194, 2793, 3464, 3703, 4470, 5021, 5308, 6219, 6866, 7897, 9384, 10175, 10582, 11421, 11852, 12739, 16098, 17129, 18736, 19287, 22166, 22765, 24612, 26531, 27850, 29889, 32000, 32719, 36438, 37205, 38764, 39555, 44474, 49681

Offset: 1

Author

Alonso del Arte, Apr 16 2012

Keywords

• nonn
• easy

Comments

One way to find a run of n consecutive nonsquarefree numbers such that the first n primes appear in order as factors of numbers in the run is to use the Chinese remainder theorem (though this run is most likely not the earliest of length n).

The moduli are then of course the squares of the first n primes, while the remainders are then the first n terms of this sequence. (See A182433.)

Examples

			a(4) = 45 because the 4th prime is 7, and 7^2 - 4 = 49 - 4 = 45.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001248 squares of primes; A045882 and A078144 pertain to runs of consecutive nonsquarefree numbers.

Cf. A014689. [Bruno Berselli, Mar 19 2013]

Programs

Magma

[NthPrime(n)^2-n: n in [1..50]]; // Bruno Berselli, Apr 16 2012

Mathematica

Table[Prime[n]^2 - n, {n, 50}]

Formula

a(n) = A000040(n)^2 - n = A001248(n) - n. - Omar E. Pol, Apr 16 2012

Extensions

a(36) inserted by Vincenzo Librandi, Mar 19 2013