A360884 a(n) = a(n-1) + a(n-2) + gcd(a(n-1), n), a(1) = a(2) = 1.

1, 1, 3, 5, 13, 19, 33, 53, 87, 141, 229, 371, 601, 973, 1575, 2549, 4125, 6677, 10803, 17481, 28287, 45769, 74057, 119827, 193885, 313713, 507625, 821339, 1328965, 2150309, 3479275, 5629585, 9108861, 14738447, 23847309, 38585765, 62433075, 101018841, 163451919, 264470761, 427922681, 692393443

Offset

1,3

Links

Table of n, a(n) for n=1..42.

Formula

a(n) = a(n-1) + a(n-2) + gcd(a(n-1), n), a(1) = a(2) = 1.

Example

a(5) = 3 + 5 + gcd(5, 5) = 13.

Maple

a:= proc(n) option remember; procname(n-1)+procname(n-2) + igcd(procname(n-1), n) end proc:
a(1):= 1: a(2):= 1:
map(a, [$1..50]); # Robert Israel, Feb 28 2023

Prog

(Python)
from math import gcd
a = [0, 1, 1]
[a.append(a[n-1]+a[n-2]+gcd(a[n-1], n)) for n in range(3, 65)]
print(a[1:])
# With help from Michael S. Branicky, Feb 25 2023

Crossrefs

Sequence in context: A081353 A238092 A024820 * A038941 A141215 A191039

Adjacent sequences: A360881 A360882 A360883 * A360885 A360886 A360887

Keyword

nonn,easy

Author

Jack Braxton, Feb 25 2023

Status

approved