Those Fascinating Numbers 131
1 493
the sixth Stern number (see the number 137).
1 518
the smallest number n such that P (n + i)

n + i, i = 0, 1, 2, 3; if nk stands
for the smallest number n such that P (n + i)

n + i, i = 0, 1, 2, . . . , k 1,
then n4 = 1 518, n5 = 5 828, n6 = 28 032, n7 = n8 = 290 783, n9 = 1 258 500
and n10 = 4 325 170; on the other hand, if mk stands for the smallest number
m such that P (m + i) (m +
i)1/k,
for i = 0, 1, 2, then m2 = 48, m3 = 134 848
and m4 = 116 026 273.
1 520
the only number n such that the set A := {1, 15, 24, n} is a diophantine quadru-
plet, that is such that xy + 1 is a perfect square for all x, y A, x = y (see the
number 120 and its footnote, as well as the number 528).
1 521 (= 32 · 132)
the smallest number n divisible by a perfect square 1 such that γ(n + 18) =
γ(n) + 18 (and there are no others 108): here we have γ(n + 18) γ(n) =
3 · 19 3 · 13 = 18;
the third odd number n 1 such that γ(n)|σ(n) (see the number 135).
1 536
the tenth Granville number (see the number 126).
1 537
the tenth Keith number (see the number 197).
1 538
the number of Niven numbers 10 000 (see the number 213).
1 540
one of the five numbers (the others are 1, 10, 120 and 7 140) which are both
triangular and tetrahedral (see the number 10).
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