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A297894 Composite numbers that divide at least one Euclid number. 0
1843, 5263, 10147, 12629, 24047, 26869, 30031, 136109, 189001, 356189, 510511, 648077, 709493, 960359, 1293109, 1459817, 1513817, 1755431, 2263607, 2290129, 2578327, 2825041, 3173707, 3415703, 3440471, 4629071, 5007641, 5497781, 5698237, 6021971, 8614843 (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. It appears that the vast majority of terms in A113165 are prime; this sequence lists the composite numbers in A113165.

No composite less than 10^8 divides more than one Euclid number.

LINKS

Table of n, a(n) for n=1..31.

EXAMPLE

a(1) = 1843 because 1843 = 19*97 is the smallest composite number that divides a Euclid number: 1843 divides 1 + A002110(7) = 1 + 2*3*5*7*11*13*17 = 510511 = 19*97*277. (Thus, 5263 (= 19*277), 26869 (= 97*277), and 19*97*277 = 510511 itself are also composites that divide a Euclid number; 5263 = a(2), 26869 = a(6), and 510511 = a(11).)

CROSSREFS

Cf. A002110 (primorials), A006862 (Euclid numbers), A113165 (numbers > 1 that divide Euclid numbers), A297891 (numbers > 1 that divide exactly two Euclid numbers).

Sequence in context: A243482 A252214 A112017 * A290393 A251109 A236160

Adjacent sequences:  A297891 A297892 A297893 * A297895 A297896 A297897

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Jan 07 2018

STATUS

approved

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Last modified November 30 21:20 EST 2021. Contains 349426 sequences. (Running on oeis4.)