

A234307


a(n) = Sum_{i=1..n} gcd(2*ni, i).


3



1, 3, 6, 8, 11, 17, 16, 20, 27, 31, 26, 44, 31, 45, 60, 48, 41, 75, 46, 80, 87, 73, 56, 108, 85, 87, 108, 116, 71, 165, 76, 112, 141, 115, 158, 192, 91, 129, 168, 196, 101, 239, 106, 188, 261, 157, 116, 256, 175, 235, 222, 224, 131, 297, 256, 284, 249, 199
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OFFSET

1,2


COMMENTS

Sum of the GCD's of the smallest and largest parts in the partitions of 2n into exactly two parts.


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Index entries for sequences related to partitions


FORMULA

a(n) = Sum_{i=1..n} gcd(2*ni, i).


EXAMPLE

a(6) = 17; the partitions of 2(6) = 12 into two parts are: (11,1),(10,2),(9,3),(8,4),(7,5),(6,6). Then a(6) = gcd(11,1) + gcd(10,2) + gcd(9,3) + gcd(8,4) + gcd(7,5) + gcd(6,6). = 1 + 2 + 3 + 4 + 1 + 6 = 17.


MAPLE

A234307:=n>add( gcd(2*ni, i), i=1..n); seq(A234307(n), n=1..100);


MATHEMATICA

Table[Sum[GCD[2n  i, i], {i, n}], {n, 100}]


PROG

(PARI) a(n) = sum(i=1, n, gcd(i, 2*ni)); \\ Michel Marcus, Dec 23 2013


CROSSREFS

Cf. A001105 (Sum of Parts), A002378 (Differences of Parts).
Sequence in context: A190430 A188018 A289241 * A175769 A160277 A233541
Adjacent sequences: A234304 A234305 A234306 * A234308 A234309 A234310


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Dec 22 2013


STATUS

approved



