Those Fascinating Numbers 293

7 774 369

• the fourth number which is equal to the sum of the seventh powers of its digits

added to the product of its digits (see the number 455 226).

7 860 799

• the largest known prime number p such that P (p2 −1) ≤ 37 and P (p2 −1) = 37:

here p2 − 1 = 27 · 32 · 52 · 11 · 173 · 29 · 372 (see the number 4 801).

7 866 046

• the fifth even number n such that

2n

≡ 2 (mod n) (see the number 161 038).

7 906 276

• the third number 1 which is both triangular and pentagonal:

7 906 272 =

3976 · 3977

2

=

2296 · (3 · 2296 − 1)

2

(see the number 210).

7 989 168

• the smallest Niven number n such that n +80 is also a Niven number, but with

no others in between (see the number 28 680).

8 382 464

• the eighth solution of σ(n) = 2n + 2 (see the number 464).

8 388 019

• the largest known regular prime (J.P. Bulher, R.E. Crandall & R.W. Sompolski

[28]).

8 489 603

• the smallest number n such that τ (n) τ (n + 1) . . . τ (n + 6): here

48 20 16 12 8 6 4 (see the number 45).

8 595 928

• the second n such that B(n)|B(n + 1) and B(n + 1)|B(n + 2), where

B(n) =

∑number

pα n

αp; the sequence of numbers satisfying this property begins

as follows: 417 162, 8 595 928, 11 506 989, 12 684 861, 20 989 800, 113 188 680,

181 665 014, . . .