A053079 a(1)=1; a(m+1) = Sum_{k=1..m} gcd(k, a(m+1-k)).

1, 1, 2, 3, 5, 5, 9, 7, 9, 17, 15, 13, 17, 15, 27, 33, 21, 27, 29, 29, 35, 33, 29, 45, 55, 51, 73, 41, 59, 61, 57, 39, 63, 57, 59, 85, 49, 87, 65, 65, 77, 93, 83, 107, 117, 73, 91, 95, 137, 97, 117, 125, 115, 131

Offset

1,3

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

a(7) = gcd(1, a(6)) + gcd(2, a(5)) + gcd(3, a(4)) + gcd(4, a(3)) + gcd(5, a(2)) + gcd(6, a(1)) = 1 + 1 + 3 + 2 + 1 + 1 = 9.

Mathematica

Fold[Append[#1, Total@Table[GCD[#1[[#2 - k]], k], {k, #2 - 1}]] &, {1}, Range[2, 54]] (* Ivan Neretin, Oct 04 2017 *)

Prog

(PARI) lista(nn) = my(va = vector(nn)); va[1] = 1; for (m=1, nn-1, va[m+1] = sum(k=1, m, gcd(k, va[m+1-k])); ); va; \\ Michel Marcus, Oct 05 2017

Crossrefs

Sequence in context: A006447 A014237 A033885 * A326061 A348203 A158901

Adjacent sequences: A053076 A053077 A053078 * A053080 A053081 A053082

Keyword

nonn

Author

Leroy Quet, Feb 25 2000

Status

approved