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A330908 a(n+1) = a(n) + (number of divisors of a(n) that are not divisors of other divisors of a(n)) for n>1; a(1)=1.

%I A330908 #26 Jul 02 2020 05:23:28
%S A330908 1,2,4,6,9,11,13,15,18,21,24,27,29,31,33,36,39,42,46,49,51,54,57,60,
%T A330908 64,66,70,74,77,80,83,85,88,91,94,97,99,102,106,109,111,114,118,121,
%U A330908 123,126,130,134,137,139,141,144,147,150,154,158,161,164,167,169
%N A330908 a(n+1) = a(n) + (number of divisors of a(n) that are not divisors of other divisors of a(n)) for n>1; a(1)=1.
%C A330908 The sequence is similar built like A094222 but includes 1 as divisor or adds 1 to the number of distinct primes dividing a(n).
%H A330908 Samuel Frankmartin-Sebastian Wiethüchter, <a href="/A330908/b330908.txt">Table of n, a(n) for n = 1..5000</a>
%F A330908 a(n) = a(n-1) + A083399(a(n-1)) for n>1.
%e A330908 For n = 2 calculate a(2)= a(2-1) + A083399(a(2-1))= 1 + 1 = 2;
%e A330908 For n = 3 a(3)=a(2) + A083399(a(2))= 2 + 2 = 4;
%e A330908 For n = 4 a(4)=a(3) + A083399(a(3))= 4 + 2 = 6;
%e A330908 For n = 5 a(5)=a(4) + A083399(a(4))= 6 + 3 = 9;
%p A330908 A330908 := proc(n) option remember;
%p A330908     if n < 2 then
%p A330908         n
%p A330908     else
%p A330908         procname(n-1)+A083399(procname(n-1))
%p A330908     end if;
%p A330908 end proc:
%p A330908 seq(A330908(n), n=1..30);
%t A330908 a[1] = 1; a[n_] := a[n] = a[n - 1] + PrimeNu[a[n - 1]] + 1; Array[a, 60] (* _Amiram Eldar_, May 01 2020 *)
%o A330908 (PARI) f(n) = omega(n) + 1; \\ A083399
%o A330908 lista(nn) = {my(a=1, va = List(a)); for (n=2, nn, a = a+f(a); listput(va, a);); Vec(va);} \\ _Michel Marcus_, May 03 2020
%Y A330908 Cf. A094222.
%K A330908 nonn
%O A330908 1,2
%A A330908 _Samuel Frankmartin-Sebastian Wiethüchter_, May 01 2020