cp's OEIS Frontend

A306312 Number of terms of the set of divisors of n that are not the product of any other two distinct divisors.

%I A306312 #13 Feb 06 2019 13:08:31
%S A306312 1,2,2,3,2,3,2,3,3,3,2,4,2,3,3,3,2,4,2,4,3,3,2,4,3,3,3,4,2,4,2,3,3,3,
%T A306312 3,5,2,3,3,4,2,4,2,4,4,3,2,4,3,4,3,4,2,4,3,4,3,3,2,5,2,3,4,3,3,4,2,4,
%U A306312 3,4,2,5,2,3,4,4,3,4,2,4,3,3,2,5,3,3,3,4
%N A306312 Number of terms of the set of divisors of n that are not the product of any other two distinct divisors.
%C A306312 Sets contain 1, primes and powers of primes.
%C A306312 a(n) <= A000005(n), a(n) <= A222084(n) and a(p) = 2 with p prime.
%C A306312 Record values for:
%C A306312 a(1) = 1
%C A306312 a(2) = 2
%C A306312 a(4) = 3
%C A306312 a(12) = 4
%C A306312 a(36) = 5
%C A306312 a(180) = 6
%C A306312 a(900) = 7
%C A306312 a(6300) = 8
%C A306312 a(44100) = 9
%C A306312 a(485100) = 10, ...
%C A306312 Records are obtained for A061742 U A228593. - _David A. Corneth_, Feb 06 2019
%e A306312 Divisors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198. Here the set is 1, 2, 3, 9, 11 because 2*3 = 6, 2*9 = 18, 2*11 = 22, 3*11 = 33, 6*11 = 66, 9*11 = 99, 2*99 = 198. Then a(198) = 5.
%p A306312 with(numtheory): with(combinat): P:=proc(q) local a,b,c,k,n;
%p A306312 for n from 2 to q do if isprime(n) then print(2) else a:=sort([op(divisors(n) minus {1})]); b:=choose(a,2); c:=[];
%p A306312 for k from 1 to nops(b) do c:=[op(c),b[k][1]*b[k][2]]; od;
%p A306312 a:=[1,op({op(a)} minus {op(c)})]; print(nops(a)); fi; od; end: P(10^6);
%o A306312 (PARI) a(n) = my(f = factor(n)[, 2]); sum(i = 1, #f, min(2, f[i])) \\ _David A. Corneth_, Feb 06 2019
%Y A306312 Cf. A000005, A061742, A222084, A228593.
%K A306312 nonn
%O A306312 1,2
%A A306312 _Paolo P. Lava_, Feb 06 2019