A364140 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared such that the sum of all terms a(1) + ... + a(n) has the same number of prime factors, counted with multiplicity, as the product of all terms a(1) * ... * a(n).

1, 2, 3, 10, 227, 77, 16064, 33464399, 8113, 3195015179, 61429, 90914613323, 71605, 2447722577897, 50167831, 66088461368723, 515670637, 33285732506297618, 94923365102, 101280524367151708435, 8787480069869, 13576059753826090424581

Offset

1,2

Comments

It is unknown if all numbers eventually appear.

Links

Table of n, a(n) for n=1..22.

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

Cf. A364139 (nondistinct terms), A001222, A027746, A364138.

Sequence in context: A055708 A162647 A368063 * A358391 A132536 A322067

Adjacent sequences: A364137 A364138 A364139 * A364141 A364142 A364143

Keyword

nonn,more

Author

Scott R. Shannon, Jul 10 2023

Extensions

a(12)-a(22) from Bert Dobbelaere, Jul 21 2023

Status

approved