278 Jean-Marie De Koninck

1 334 961

• the number of possible arrangements of the integers 1,2,. . . ,10 with the restric-

tion that the integer j must not be in the j-th position for each j, 1 ≤ j ≤ 10

(see the number 265).

1 362 239

• the sixth solution of σ2(n) = σ2(n + 2) (see the number 1 079).

1 373 653

• the smallest strong pseudoprime with respect to bases 2 and 3.

1 398 269

• the exponent of the

35th

Mersenne prime

21 398 269

− 1 (Armengaud, 1996):

G.F. Woltman wrote a programme based on the Lucas-Lehmer test and made

it accessible on the WEB (see www.mersenne.org) for anyone who wants to find

the largest Mersenne prime; the 36th (22 976 220 − 1), 37th (23 021 377 − 1), 38th

(26 972 593 − 1), 39th (213 477 966 − 1), 40th (220,996 011 − 1), 41rst (224 036 583 − 1),

42nd (225 964 951−1), 43rd (230 402 457−1), 44th (232 582 657−1), 45th (237 156 667−1)

and 46th (243 112 609 − 1) Mersenne primes have been found by volunteers using

Woltman’s programme.

1 413 721

• the fifth number which is both a triangular number and a perfect square:

1 413 721 =

1681(1681+1)

2

=

11892

(see the number 36).

1 416 329

• the smallest prime number q such that

∑

p≤q

p is divisible by 510 510 (= 2 · 3 ·

5 · 7 · 11 · 13 · 17): here this sum is equal to 73 454 220 840 (see the number 269).

1 419 263

• the largest known prime number p such that P

(p2

−1) ≤ 19 and P

(p2

−1) = 19:

here 1 419 2632 − 1 = 212 · 32 · 7 · 11 · 133 · 17 · 19 (see the number 4 801).

1 441 440

• the 12th colossally abundant number (see the number 55 440).