Those Fascinating Numbers 223

59 535

• the second solution of γ(n + 1) − γ(n) = 17 (see the number 1 681).

59 656

• the eighth number n 1 such that n ·

2n

+ 1 is prime (see the number 141).

60 228

• the seventh number n such that σ(n) and σ2(n) have the same prime factors,

namely the primes 2, 3, 5, 7 and 13 (see the number 180).

62 244

• the fifth number n such that each of the numbers n + i, i = 0, 1, 2, . . . , 16, have

a factor in common with the other 16 (see the number 2 184).

62 471

• (probably) the largest number which cannot be written as the sum of two co-

prime numbers whose index of composition is ≥ 1.8 (see the number 933).

64 210

• the smallest number n such that

∑

m≤n

σ(m) is a multiple of 100 000 (and of

1 000 000): here the sum is equal to 1 391 000 000.

64 540

• the smallest number n such that π(n) = n/10 (see the number 330).

64 890

• the second solution of σ(n) = 3n + 18 (see the number 17 850).

64 980

• the eighth number n such that σ(n) and σ2(n) have the same prime factors,

namely the primes 2, 3, 7, 13 and 127 (see the number 180).

65 024

• the fifth number n divisible by a square 1 and such that γ(n + 1) − γ(n) = 1

(see the number 48).