A392530 a(1) = 1; for n > 1, a(n) is the smallest unused number such that the sum a(1) + ... + a(n) is coprime to the product a(1) * ... * a(n), where both the sum and product are nonprime.

1, 8, 16, 2, 22, 20, 50, 4, 10, 26, 44, 34, 64, 32, 28, 56, 112, 14, 46, 68, 122, 52, 62, 40, 74, 70, 170, 82, 58, 80, 110, 94, 172, 86, 104, 100, 280, 116, 302, 118, 148, 92, 98, 124, 140, 78, 134, 18, 88, 368, 162, 142, 176, 166, 258, 188, 24, 214, 200, 66, 156

Offset

1,2

Comments

As the product is always even, all terms beyond a(2) must also be even to ensure that the sum of all terms is odd.

In the first 10000 terms all even numbers less than 12658 appear; it is likely the sequence contains all even numbers.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^14, with a color function showing 1 in black, primes in red, proper prime powers in gold, squarefree composites in green, powerful numbers that are not prime powers in purple, and numbers that are neither powerful nor squarefree in blue.

Example

a(5) = 22 as the sum of all terms a(1) to a(6) = 1 + 8 + 16 + 2 + 22 = 49 = 7^2 which is coprime to the product of all terms 1 * 8 * 16 * 2 * 22 = 5632 = 2^9 * 11.

Mathematica

Block[{c, k, s, p, u, nn}, nn = 120; c[_] := False; k = s = p = 1; c[1] = True; u = 2; {k}~Join~Reap[Do[k = u; While[Or[c[k], ! CoprimeQ[s + k, p*k], AnyTrue[{s + k, p*k}, PrimeQ]], k += 2]; c[k] = True; Sow[k]; s += k; p *= k; If[k == u, While[c[u], u += 2] ], {n, 2, nn}] ][[-1, 1]] ] (* Michael De Vlieger, Feb 21 2026 *)

Crossrefs

Cf. A390314, A018252, A073659, A000040, A027748.

Sequence in context: A387555 A073926 A396608 * A073925 A053321 A335772

Adjacent sequences: A392527 A392528 A392529 * A392531 A392532 A392533

Keyword

nonn

Author

Scott R. Shannon, Feb 20 2026

Status

approved