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A297891 Numbers that divide exactly two Euclid numbers. 3
277, 1051, 1381, 1657, 1867, 3001, 3373, 3499, 4637, 4877, 5147, 6673, 7547, 10859, 10987, 14797, 17291, 18749, 19531, 25939, 27337, 27953, 31013, 32203, 32983, 33547, 34123, 34591, 35747, 38047, 38197, 38711, 44293, 44357, 47059, 47569, 48809, 51151, 51437 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The k-th Euclid number, A006862(k), is 1 plus the product of the first k primes, i.e., 1 + A002110(k). A113165 lists the numbers (> 1) that divide at least one Euclid number; a(1) = 277 = A113165(19); a(2) = 1051 = A113165(41); a(53) = 92143 = A113165(995).

Up to N = 10^5, roughly 5% of the terms in A113165 are also in this sequence. Does that ratio continue to hold as N increases?

It appears that the vast majority of terms in A113165 are prime, but that sequence contains a number of composite numbers as well, beginning with A113165(59) = 1843 = 19*97, A113165(125) = 5263 = 19*277, A113165(195) = 10147 = 73*139, and A113165(231) = 12629 = 73*173. But do any composites divide more than one Euclid number?

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..1000

EXAMPLE

a(1) = 277 because 277 is the smallest number that divides exactly two Euclid numbers: 1 + 2*3*5*7*11*13*17 = 510511 and 1 + 2*3*5*7*11*13*17*19*23*29*31*37*41*43*47*53*59 = 1922760350154212639071.

CROSSREFS

Cf. A002110 (primorials), A006862 (Euclid numbers), A113165 (numbers > 1 that divide Euclid numbers).

Sequence in context: A142127 A142831 A105977 * A236803 A048525 A189609

Adjacent sequences:  A297888 A297889 A297890 * A297892 A297893 A297894

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Jan 07 2018

STATUS

approved

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Last modified May 24 17:54 EDT 2022. Contains 354043 sequences. (Running on oeis4.)