Those Fascinating Numbers 297
11 350 529
the smallest prime number p such that Ω(p 1) = Ω(p + 1) = 11: here
11 350 528 = 29 · 7 · 3167 and 11 350 530 = 2 · 38 · 5 · 173 (see the number
271).
11 506 989
the fifth number n such that β(n)|β(n +1) and β(n +1)|β(n +2), here 381|1524
and 1524|12192 (see the number 225 504).
11 746 427
the fourth number n for which ξ(n) is an integer (see the number 614 341).
11 859 210
the smallest number n such that P (n)4|n and P (n+1)4|n+1: here 11 859 210 =
2 · 34 · 5 · 114 and 11 859 211 = 7 · 13 · 194; other numbers satisfying this property
are 632 127 050 601 113 666 430, 1 337 735 048 956 150 266 042 387,
2 512 088 574 784 743 818 066 896 4 974 823 008 148 736 705 412 779,
33 604 891 766 609 212 616 768 123 and 34 120 594 939 631 428 731 879 552 (see the
number 6 859).
12 204 889
the first term of the smallest sequence of 13 consecutive prime numbers all of
the form 4n + 1 (see the number 2 593).
12 270 077
the first term of the smallest sequence of 14 consecutive prime numbers all of
the form 4n + 1 (as well as for 15 or 16 consecutive prime numbers of the form
4n + 1) (see the number 2 593).
12 558 912
the
14th
number n such that φ(n) + σ(n) = 3n (see the number 312).
12 582 633
the smallest number n such that ω(n) + ω(n + 1) + ω(n + 2) + ω(n + 3) = 20:
here 12 582 633 = 3 · 7 · 23 · 109 · 239, 12 582 634 = 2 · 83 · 229 · 331, 12 582 635 =
5 · 13 · 17 · 59 · 193 and 12 582 636 =
22
· 3 · 11 · 19 · 29 · 173 (see the number 987).
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