352 Jean-Marie De Koninck
12 973 363 226
the only number 2 which is equal to the sum of the factorials of its digits
in base 14: here 12 973 363 226 = [8, 11, 0, 13, 13, 4, 0, 9, 12]14 = 8! + 11! + 0! +
13! + 13! + 4! + 0! + 9! + 12! (see also the numbers 145 and 40 472).
13 051 463 048
the 15th powerful number n such that n+1 is also powerful: here 13 051 463 048 =
23 · 134 · 2392 and 13 051 463 049 = 32 · 1132 · 3372 (see the number 288).
13 272 412 062 (= 2 · 3 · 7 · 13 · 23 · 47 · 113 · 199)
the
14th
ideal number (see the number 390).
13 544 168 521 (=
132
· 2347 · 34147)
the sixth 12-hyperperfect number (see the number 697).
14 182 439 040 (= 27 · 34 · 5 · 7 · 112 · 17 · 19)
the smallest 5-perfect number: n is 5-perfect if σ(n) = 5n; the second one is
31 998 395 520; many believe that there exist only 65 5-perfect numbers (see
R.K. Guy [104], B2).
14 872 568 831
the smallest number n which allows the sum
i≤n
1
i
to exceed 24 (see the number
83).
14 924 714 400 (= 25 · 33 · 52 · 312 · 719)
the largest known number n such that φ(n) + σ(n) = 4n (see the number
23 760).
15 527 402 881
the smallest fourth power which can be written as the sum of four fourth powers:
15 527 402 881 = 3534 = 304 + 1204 + 2724 + 3154.
15 834 664 872
the number of twin prime pairs 1013 (see the number 1 224).
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