A297894 Composite numbers that divide at least one Euclid number.

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

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