

A252493


Numbers n such that n(n+1) is 13smooth. (Related to the abc conjecture.)


9



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 24, 25, 26, 27, 32, 35, 39, 44, 48, 49, 54, 55, 63, 64, 65, 77, 80, 90, 98, 99, 104, 120, 125, 143, 168, 175, 195, 224, 242, 324, 350, 351, 363, 384, 440, 539, 624, 675, 728, 1000, 1715, 2079, 2400, 3024, 4095, 4224, 4374, 6655, 9800, 10647, 123200
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OFFSET

1,2


COMMENTS

Equivalently: Numbers n such that all prime factors of n and n+1 are <= 13, i.e., both are in A080197.
This sequence is complete by a theorem of Stormer, cf. A002071.
This is the 6th row of the table A138180. It has 68=A002071(6)=A145604(1)+...+ A145604(6) terms and ends with A002072(6)=123200. It is the union of all terms in rows 1 through 6 of the table A145605.
Contains A085152, A085153, A252494 as subsequences.


LINKS

Table of n, a(n) for n=1..68.
Abderrahmane Nitaj, The ABC conjecture homepage
OEIS Index entries for sequences related to the abc conjecture


MAPLE

N:= 130000: # to get all entries <= N
f:= proc(n)
uses padic;
evalb(2^ordp(n, 2)*3^ordp(n, 3)*5^ordp(n, 5)*7^ordp(n, 7)*11^ordp(n, 11)*13^ordp(n, 13) = n)
end proc:
L:= map(f, [$1..N+1]):
select(t > L[t] and L[t+1], [$1..N]); # Robert Israel, Jan 16 2015


MATHEMATICA

Select[Range[123456], FactorInteger[ # (# + 1)][[ 1, 1]] <= 13 &]


PROG

(PARI) for(n=1, 123456, vecmax(factor(n++, 13)[, 1])<17 && vecmax(factor(n+(n<2), 13))<17 && print1(n", ")) \\ Skips the next n if n+1 is not 13smooth: Twice as fast as the naïve version. Instead of vecmax(.)<17 one could use is_A080197().


CROSSREFS

Cf. A002071, A145604, A138180, A145605, A002072, A085152, A085153, A252493, A252492.
Sequence in context: A246096 A098314 A052057 * A005496 A052060 A084688
Adjacent sequences: A252490 A252491 A252492 * A252494 A252495 A252496


KEYWORD

nonn,fini,full


AUTHOR

M. F. Hasler, Jan 16 2015


STATUS

approved



