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

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

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).

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 *)

Prog

(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));

Crossrefs

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

Cf. also A353361.

Sequence in context: A082498 A112223 A324810 * A178771 A289498 A193929

Adjacent sequences: A353348 A353349 A353350 * A353352 A353353 A353354

Keyword

nonn

Author

Antti Karttunen, Apr 15 2022

Status

approved