A252492 The largest prime factor of n*(n+1) equals 17. (Related to the abc conjecture.)

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

Offset: 1

Author

M. F. Hasler, Jan 16 2015

Keywords

• nonn
• fini
• full

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

• OEIS Index entries for sequences related to the abc conjecture

Crossrefs

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

Programs

Mathematica

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

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.