A230120 a(n) is the number of evil integers (A001969) not exceeding n and prime to n.

0, 0, 0, 1, 1, 1, 3, 2, 1, 2, 5, 1, 6, 3, 0, 4, 7, 2, 9, 3, 4, 5, 10, 3, 8, 6, 5, 7, 13, 3, 15, 8, 6, 8, 12, 4, 18, 9, 7, 8, 20, 4, 20, 10, 5, 11, 23, 5, 24, 9, 8, 12, 25, 6, 19, 14, 11, 14, 29, 5, 30, 15, 12, 16, 22, 7, 33, 15, 12, 12, 34, 8, 36, 18, 10, 18

Offset

1,7

Comments

See comment in A230070, taking into account the equality a(n) = phi(n) - A230070(n), where phi(n) is Euler totient function (A000010).

Links

Georg Fischer, Table of n, a(n) for n = 1..5000

Formula

For odd evil prime p (A027699), a(p) = (p-3)/2; for odd odious prime p (A027697), a(p) = (p-1)/2.

Mathematica

upTo[n_] := Block[{c, i, e = Select[Range[n], EvenQ@ DigitCount[#, 2, 1] &]}, Table[c = 0; i = 1; While[i <= Length@ e && e[[i]] < k, c += Boole@ CoprimeQ[e[[i]], k]; i++]; c, {k, n}]]; upTo[100] (* Giovanni Resta, Apr 14 2025 *)

Prog

(PARI) a(n) = sum(k = 1, n, gcd(k, n) == 1 && !(hammingweight(k) % 2)); \\ Amiram Eldar, Nov 10 2024

Crossrefs

Cf. A000010, A001969, A230070, A027697, A027699.

Sequence in context: A240485 A048984 A329587 * A360872 A136531 A127318

Adjacent sequences: A230117 A230118 A230119 * A230121 A230122 A230123

Keyword

nonn,base,easy

Author

Vladimir Shevelev, Oct 10 2013

Status

approved