Those Fascinating Numbers 329

367 567 200 (= 25 · 33 · 52 · 7 · 11 · 13 · 17)

• the

15th

colossally abundant number (see the number 55 440).

370 851 481 (=7 · 11 · 13 · 17 · 19 · 31 · 37)

• the smallest pseudoprime in base 2 having seven prime factors (see the number

11 305).

378 043 979

• the smallest prime number p such that p + 200 is prime and such that each

number between p and p + 200 is composite (see the number 396 733).

384 199 200

• the

11th

powerful number n such that n +1 is also powerful: here 384 199 200 =

25

·

34

·

52

·

72

·

112

and 384 199 201 =

172

·

11532

(see the number 288).

387 420 490 (= 2 · 5 · 73 · 530713)

• the ninth number of the form

nn

+ 1 (see the number 3 126).

391 854 937 (= 547 · 569 · 1259)

• the third hyperperfect number which is the product of three distinct prime

numbers: it happens to be a 228-hyperperfect number (see the number 21).

395 096 427 (=

33

· 11 · 43 · 30937)

• the number n which allows the sum

m≤n

Ω(m)=6

1

m

to exceed 1 (see the number

874 660).

402 831 360

• the seventh number n such that φ(n) + σ(n) = 4n (see the number 23 760).

404 204 977

• the number of ten digit prime numbers (see the number 21).

405 071 317

• the value of 11 + 22 + . . . + 99 (see the number 3 413).