Those Fascinating Numbers 47
the smallest solution of σ(n) = σ(n + 38); the sequence of numbers satisfying
this equation begins as follows: 147, 246, 249, 460, 627, 715, 716, 1026, 1509,
2427, 4857, 5396, 6815, 6954, 8672, 9447, 9714, 9752,. . . ;
the second composite number n such that σ(n + 6) = σ(n) + 6 (see the number
104).
152
the second solution of γ(n + 1) γ(n) = 13: the only solutions n 109 of this
equation are 18, 152 and 3 024 (see the footnote tied to the number 98).
153
the second number which can be written as the sum of the cubes of its digits:
153 = 13 + 53 + 33; the others are 1, 370, 371 and 407;
the smallest narcissistic number of more than one digit (see the number 88);
the largest known number k such that the decimal expansion of 2k does not
contain the digit 3; indeed, using a computer, one can verify that
2153
= 11417981541647679048466287755595961091061972992
does not contain the digit 3, while each number 2k, for k = 154, 155, . . . , 3000,
contains it (see the number 71);
the value of 1! + 2! + 3! + 4! + 5! .
154
the rank of the prime number which appears the most often as the 11th prime
factor of an integer : p154 = 887 (see the number 199);
the 11th number n such that n! + 1 is prime (see the number 116).
155
the number of digits in the decimal expansion of the Fermat number
229
+ 1,
a number whose complete factorization was obtained in 1990 (see the number
70 525 124 609).
156
the second number n 1 which divides σ8(n) (see the number 84).
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