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A353351 Number of divisors d of n for which A048675(d) is not a multiple of 3.

%I A353351 #13 Apr 19 2022 11:41:14
%S A353351 0,1,1,2,1,2,1,2,2,3,1,4,1,2,2,3,1,4,1,4,3,3,1,5,2,2,2,4,1,5,1,4,2,3,
%T A353351 2,6,1,2,3,5,1,5,1,4,4,3,1,6,2,4,2,4,1,5,3,5,3,2,1,8,1,3,4,4,2,5,1,4,
%U A353351 2,5,1,8,1,2,4,4,2,5,1,7,3,3,1,8,3,2,3,5,1,8,3,4,2,3,2,8,1,4,4,6,1,5,1,5,5
%N A353351 Number of divisors d of n for which A048675(d) is not a multiple of 3.
%H A353351 Antti Karttunen, <a href="/A353351/b353351.txt">Table of n, a(n) for n = 1..65537</a>
%H A353351 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353351 a(n) = Sum_{d|n} (1-A353350(d)).
%F A353351 a(n) = A000005(n) - A353352(n).
%F A353351 a(p) = 1 for all primes p.
%F A353351 a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
%F A353351 a(n) = A353328(n) + A353329(n).
%t A353351 f[p_, e_] := e*2^(PrimePi[p] - 1); q[1] = False; q[n_] := ! Divisible[Plus @@ f @@@ FactorInteger[n], 3]; a[n_] := DivisorSum[n, 1 &, q[#] &]; Array[a, 100] (* _Amiram Eldar_, Apr 15 2022 *)
%o A353351 (PARI)
%o A353351 A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
%o A353351 A353350(n) = (0==(A048675(n)%3));
%o A353351 A353351(n) = sumdiv(n,d,!A353350(d));
%Y A353351 Cf. A000005, A003961, A048675, A332820, A348717, A353328, A353329, A353350, A353352, A353354.
%Y A353351 Cf. also A353361.
%K A353351 nonn
%O A353351 1,4
%A A353351 _Antti Karttunen_, Apr 15 2022