A330070 a(n) is the smallest integer k > 1 such that k cannot be expressed as a sum of distinct earlier terms nor is a multiple of any earlier term.

2, 3, 7, 11, 17, 25, 59, 67, 185, 193, 563, 571, 1697, 1747, 5141, 5149, 11995, 25727, 27439, 78893, 82345, 240131, 243583, 723845, 727297, 2174987, 2178439, 6530119, 6530123, 13061947, 19590377, 39182441, 52242689, 91425127, 195910507, 235092943, 626913953

Offset

1,1

Comments

Conjecture: Composite terms k greater than 25 will have either two or six nontrivial divisors (that is, divisors d with 1 < d < k).

The total numbers of divisors of the first 31 terms are 2, 2, 2, 2, 2, 3, 2, 2, 4, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2, 8, 2, 2, 8, 2, 4, 2, 8, 4, 2, 2. - N. J. A. Sloane, Dec 01 2019

Links

Rémy Sigrist and Giovanni Resta, Table of n, a(n) for n = 1..48

Rémy Sigrist, C++ program for A330070

Example

a(6) = 25 = 5 * 5: 5 is not in the sequence, and no combination of 2, 3, 7, 11, and 17 sums to 25.

Prog

(C++) See Links section.

Crossrefs

Cf. A330071, A330126.

Sequence in context: A045325 A216825 A094066 * A350839 A161921 A060341

Adjacent sequences: A330067 A330068 A330069 * A330071 A330072 A330073

Keyword

nonn

Author

J. Stauduhar, Nov 30 2019

Extensions

Terms a(24)-a(31) from Christian Lawson-Perfect, Dec 01 2019

Terms a(32)-a(37) from Rémy Sigrist, Dec 02 2019

Status

approved