A364139 a(1) = 1; for n > 1, a(n) is the smallest positive number 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, 2, 73, 15, 8096, 36661237, 6155, 92464579, 113213, 2195269558, 5412938, 656672315917, 27764211, 296739271898493, 1339787907, 4052257753377273867, 1371296237557, 68893436230026358982, 12176387510074, 35378806473679275300836, 4512548469598236, 28260736731720477851055640182

Offset

1,2

Comments

Other than a(2) = a(4) = 2, it is unknown if more terms appear with the same value, or if all numbers eventually appear.

Links

Table of n, a(n) for n=1..24.

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) + 3 = 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) = 2 as a(1) + a(2) + a(3) + 2 = 1 + 2 + 3 + 2 = 8 = 2^3, while a(1) * a(2) * a(3) * 2 = 1 * 2 * 3 * 2 = 12 = 2^2 * 3, both of which have three prime factors.
a(13) = 5412938 as a(1) + ... + a(12) + 5412938 = 2329935872 = 2^21 * 11 * 101, while a(1) * ... * a(12) * 5412938 = 2986...7200 = 2^9 * 3^2 * 5^2 * 11 * 23 * 73 * 139 * 1231 * 19471 * 113213 * 36661237 * 92464579 * 1097634779, both of which have twenty-three prime factors.

Crossrefs

Cf. A364140 (distinct terms), A001222, A027746, A364137.

Sequence in context: A291489 A075121 A075108 * A265590 A260208 A242457

Adjacent sequences: A364136 A364137 A364138 * A364140 A364141 A364142

Keyword

nonn

Author

Scott R. Shannon, Jul 10 2023

Extensions

a(14)-a(24) from Bert Dobbelaere, Jul 21 2023

Status

approved