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a(1)=1. Thereafter, a(n) = n*a(n-1) if the number of divisors of n*a(n-1) is <= the number of divisors of n+a(n-1) or a(n) = n+a(n-1) if n*a(n-1) has more divisors than n+a(n-1).
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%I #12 Oct 17 2014 22:51:57

%S 1,2,5,9,14,20,27,35,44,54,65,77,1001,1015,1030,1046,1063,1081,20539,

%T 20559,431739,431761,9930503,9930527,248263175,248263201,248263228,

%U 248263256,248263285,248263315,248263346,248263378,248263411,8440955974,8440956009

%N a(1)=1. Thereafter, a(n) = n*a(n-1) if the number of divisors of n*a(n-1) is <= the number of divisors of n+a(n-1) or a(n) = n+a(n-1) if n*a(n-1) has more divisors than n+a(n-1).

%e a(12)+13 = 77 + 13 = 90. a(12)*13 = 77 * 13 = 1001. 90 has 12 divisors. 1001 has 8 divisors. Since 1001 has fewer divisors than 90, a(13) is 1001.

%o (PARI) lista(nn) = {preca = 1; print1(preca, ", "); for (i = 2, nn, if (numdiv(p=i*preca) <= numdiv(s=i+preca), nexta = p, nexta = s); print1(nexta, ", "); preca = nexta;);} \\ _Michel Marcus_, Feb 10 2014

%Y Cf. A134190.

%K nonn

%O 1,2

%A _Leroy Quet_, Oct 12 2007

%E More terms from _Michel Marcus_, Feb 10 2014