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

Author

Vladimir Shevelev, Oct 10 2013

Keywords

• nonn
• base
• easy

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

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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