A330071 -id:A330071 - cp's OEIS frontend

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

J. Stauduhar, Nov 30 2019

nonn

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

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

Rémy Sigrist and Giovanni Resta, Table of n, a(n) for n = 1..48
Rémy Sigrist, C++ program for A330070

Cf. A330071, A330126.

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

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

A330126 Composite terms in A330070.

Original entry on oeis.org

25, 185, 5141, 5149, 11995, 25727, 27439, 82345, 723845, 2174987, 6530119, 6530123, 39182441, 91425127, 195910507, 235092943, 626913953, 1293010349, 5158981145, 16756893533, 18036843631, 51550630699, 103284111653, 104537939563, 207665323147

Offset: 1

Giovanni Resta, Dec 02 2019

nonn

Cf. A330070, A330071.

cp's OEIS Frontend

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.

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A330126 Composite terms in A330070.

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