Those Fascinating Numbers 121
1 187
the fifth Stern number (see the number 137).
1 189
the fourth solution w of the aligned houses problem (see the number 35).
1 197
the 1
000th
composite number (see the number 133).
1 201
the fourth prime number of the form
(x4
+
y4)/2:
here 1 201 =
(14
+
74)/2
(see
the number 41).
1 210
the number which, when paired with the number 1 184, forms an amicable pair
(see the number 1 184).
1 215
the smallest number n such that n and n +1 are both divisible by a fifth power:
1215 = 35 · 5, 1216 = 26 · 19; if nk stands for the smallest number n such that n
and n + 1 are both divisible by a kth power, then n2 = 8, n3 = n4 = 80, n5 =
1 215, n6 = 16 767, n7 = 76 544, n8 = 636 416, n9 = 3 995 648, n10 = 24 151 040
and n11 = 36 315 135 (for the analogue problem concerning three consecutive
integers, see the number 1 375).
1 218 (= 2 · 3 · 7 · 29)
the smallest solution of
φ(n)
n
=
8
29
; the sequence of numbers satisfying this
equation begins as follows: 1218, 2436, 3654, 4872, 7308, 8526, 9744, . . . ; it is
easy to establish that this sequence is infinite123.
123Indeed,
this follows from the fact that one can easily prove that n is a solution of this equation
if and only if n = · · · 29δ for certain positive integers α, β, γ, δ.
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