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%I #24 Mar 04 2023 15:14:05
%S 1,1,3,5,13,19,33,53,87,141,229,371,601,973,1575,2549,4125,6677,10803,
%T 17481,28287,45769,74057,119827,193885,313713,507625,821339,1328965,
%U 2150309,3479275,5629585,9108861,14738447,23847309,38585765,62433075,101018841,163451919,264470761,427922681,692393443
%N a(n) = a(n-1) + a(n-2) + gcd(a(n-1), n), a(1) = a(2) = 1.
%F a(n) = a(n-1) + a(n-2) + gcd(a(n-1), n), a(1) = a(2) = 1.
%e a(5) = 3 + 5 + gcd(5, 5) = 13.
%p a:= proc(n) option remember; procname(n-1)+procname(n-2) + igcd(procname(n-1),n) end proc:
%p a(1):= 1: a(2):= 1:
%p map(a, [$1..50]); # _Robert Israel_, Feb 28 2023
%o (Python)
%o from math import gcd
%o a = [0, 1, 1]
%o [a.append(a[n-1]+a[n-2]+gcd(a[n-1], n)) for n in range(3, 65)]
%o print(a[1:])
%o # With help from _Michael S. Branicky_, Feb 25 2023
%K nonn,easy
%O 1,3
%A _Jack Braxton_, Feb 25 2023