A266580 Numerator of the continued fraction [n; p(1), p(2), p(3),..., p(m)], where n = Product_{k=1..m} p(k), m = bigomega(n), p(1)<=p(2)<=p(3)<=...<=p(m-1)<=p(m), sigma_0(p(k)) = 2.

5, 10, 22, 26, 45, 50, 101, 93, 115, 122, 211, 170, 217, 245, 476, 290, 424, 362, 551, 469, 517, 530, 1001, 655, 715, 901, 1051, 842, 1126, 962, 2269, 1133, 1207, 1267, 2039, 1370, 1501, 1573, 2627, 1682, 2164, 1850, 2531, 2401, 2185, 2210, 4793, 2457, 2876, 2669, 3511, 2810, 4137, 3091

Offset

2,1

Comments

a(n) = n^2 + 1 if n is prime (A000040).

Denominators give the sequence: b(n) = 2, 3, 5, 5, 7, 7, 12, 10, 11, 11, 17, 13, 15, 16, 29, 17, 23, 19, 27, 22, 23, 23, 41, 26, 27, 33, 37, 29, 37, 31, 70, 34, 35, 36, 56, 37, 39, 40, 65, 41, 51, 43, 57, 53, 47, 47, 99, 50, 57, 52, 67, 53, 76, 56, ...; where b(n) = n if n is prime.

Links

Table of n, a(n) for n=2..55.

Ilya Gutkovskiy, Extended example

Eric Weisstein's World of Mathematics, Prime Factor

Example

5/2, 10/3, 22/5, 26/5, 45/7, 50/7, 101/12, 93/10, 115/11, 122/11, 211/17, 170/13, 217/15, 245/16, 476/29, 290/17, 424/23, 362/19, 551/27, 469/22, ...
a(20) = 551, because the prime factorization of 20 is 2*2*5 and 20 + 1/(2 + 1/(2 + 1/5)) = 551/27.

Mathematica

Numerator@ Table[ FromContinuedFraction@ Flatten[ {{n}, Table[#[[1]], {#[[2]]}] & /@ FactorInteger@n}], {n, 2, 55}] (* Giovanni Resta, May 21 2016 *)

Crossrefs

Cf. A000040, A001222, A027746.

Sequence in context: A297301 A132461 A255150 * A271257 A343456 A087746

Adjacent sequences: A266577 A266578 A266579 * A266581 A266582 A266583

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 07 2016

Extensions

Missing a(28) added by Giovanni Resta, May 21 2016

Status

approved