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A252492 The largest prime factor of n*(n+1) equals 17. (Related to the abc conjecture.) 7
16, 17, 33, 34, 50, 51, 84, 119, 135, 153, 169, 220, 255, 272, 288, 374, 441, 560, 594, 714, 832, 935, 1088, 1155, 1224, 1274, 1700, 2057, 2430, 2499, 2600, 4913, 5831, 12375, 14399, 28560, 31212, 37179, 194480, 336140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, the prime factors of n and n+1 are not larger than 17, but not all smaller than 17 (in which case n is in A252493).

This sequence is complete by a theorem of Stormer, cf. A002071 and sequences A085152, A085153, A252494, A252493.

This is row 7 of A145605. It has A145604(7)=40 terms and ends with A002072(7)=336140.

LINKS

Table of n, a(n) for n=1..40.

OEIS Index entries for sequences related to the abc conjecture

MATHEMATICA

Select[Range[345678], FactorInteger[ # (# + 1)][[ -1, 1]] == 17 &]

PROG

(PARI) for(n=1, 9e6, vecmax(factor(n++)[, 1])<18 && vecmax(factor(n*n--)[, 1])==17 && print1(n", ")) \\ Skips 2 if n+1 is not 17-smooth: Twice as fast as the naïve version.

CROSSREFS

Cf. A002473, A086247, A252493, A252494, A085153, A085152.

Sequence in context: A241751 A244431 A151977 * A319281 A022106 A041518

Adjacent sequences:  A252489 A252490 A252491 * A252493 A252494 A252495

KEYWORD

nonn,fini,full

AUTHOR

M. F. Hasler, Jan 16 2015

STATUS

approved

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Last modified November 18 14:55 EST 2019. Contains 329262 sequences. (Running on oeis4.)