OFFSET
1,2
COMMENTS
It is unknown if all numbers eventually appear.
EXAMPLE
a(2) = 2 as a(1) + 2 = 1 + 2 = 3 while a(1) * 2 = 1 * 2 = 2, both of which have one prime factor.
a(3) = 3 as a(1) + a(2) + 4 = 1 + 2 + 3 = 6 = 2 * 3 while a(1) * a(2) * 3 = 1 * 2 * 3 = 6 = 2 * 3, both of which have two prime factors.
a(4) = 10 as a(1) + a(2) + a(3) + 10 = 1 + 2 + 3 + 10 = 16 = 2^4, while a(1) * a(2) * a(3) * 10 = 1 * 2 * 3 * 10 = 60 = 2^2 * 3 * 5, both of which have four prime factors.
a(11) = 61429 as a(1) + ... + a(10) + 61429 = 3228565504 = 2^20 * 307, while a(1) * ... * a(10) * 61429 = 8977...7120 = 2^8 * 3 * 5 * 7^2 * 11 * 19 * 47 * 61 * 227 * 251 * 1307 * 33464399 * 3195015179, both of which have twenty-one prime factors.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, Jul 10 2023
EXTENSIONS
a(12)-a(22) from Bert Dobbelaere, Jul 21 2023
STATUS
approved