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URL: https://oeis.org/A353351

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A353351
Number of divisors d of n for which A048675(d) is not a multiple of 3.
5
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
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));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 15 2022
STATUS
approved