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

1,1

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.)

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

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

Sequence in context: A158236 A174942 A128599 * A080882 A229807 A229900

Adjacent sequences: A182171 A182172 A182173 * A182175 A182176 A182177

Keyword

nonn,easy

Author

Alonso del Arte, Apr 16 2012

Extensions

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

Status

approved