190 Jean-Marie De Koninck

13 224

• the smallest Sastry number made up of five digits (see the number 6 099).

13 365

• the 20th solution of φ(n) = φ(n + 1) (see the number 15).

13 367

• the smallest prime factor of the Mersenne number 241 − 1 (Plana, 1863), whose

complete factorization is given by

241

− 1 = 13 367 · 164 511 353.

13 456

• the only solution n

1012

of σ(n) = 2n + 89.

13 649

• the 15th prime number pk such that p1p2 . . . pk + 1 is prime (see the number

379).

13 650

• the second solution of φ(n + 1) = 4φ(n) (see the number 1 260).

13 691

• the second prime number p such that 83p−1 ≡ 1 (mod p2) (see the number

4 871).

13 775

• the third number n such that n2+2 is powerful: here 13 7752+2 = 189 750 627 =

33 · 112 · 2412 (see the number 265).

13 783

• the fifth number which does not produce a palindrome by the 196-algorithm

(see the number 196).