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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Apr 15 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000005, A003961, A048675, A332820, A348717, A353328, A353329, A353350, A353352, A353354.

Cf. also A353361.

Programs

Mathematica

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 *)

PARI

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A353350(n) = (0==(A048675(n)%3));
A353351(n) = sumdiv(n,d,!A353350(d));

Formula

a(n) = Sum_{d|n} (1-A353350(d)).

a(n) = A000005(n) - A353352(n).

a(p) = 1 for all primes p.

a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.

a(n) = A353328(n) + A353329(n).