Those Fascinating Numbers 107
834
the rank of the prime number which appears the most often as the 15th prime
factor of an integer: p834 = 6397 (see the number 199).
836
the second bizarre number (see the number 70);
the fourth number which is not a palindrome, but whose square is a palindrome
(see the number 26).
839
the smallest prime factor of the Mersenne number 2419 1.
840 (=
23
· 3 · 5 · 7)
the largest number n such that
pn
p |n
1
p
1: here this sum is approximately
0.997975. . . ;
the
15th
highly composite number (see the number 180).
841 (= 292)
the smallest powerful number which can be written as the sum of two co-prime
3-powerful numbers = 1 (a number n is said to be k-powerful if p|n =⇒ pk|n):
here
292
= 841 = 216 + 625 =
23
·
33
+
54;
the sequence of numbers satisfying
this property begins as follows: 841, 968, 2312, 3528, 5041, 5776, 12769, 14884,
16641, 45125, 51984, . . .
843
the smallest number n such that
f(n + 1) = f(n + 2) = f(n + 3) = f(n + 4),
where f(n) stands for the product of the exponents in the factorization of n:
here the common value of f(n + i) is 2; if for each number k 2, we denote by
nk the smallest positive integer n such that
f(n + 1) = f(n + 2) = . . . = f(n + k),
we then have the following table:
k 2 3 4 5 6 7
nk 1 4 843 74 848 671 345 8 870 024
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