A332903 a(1) = 1, then after the first differences of A333123.

1, 0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 1, 0, 2, 0, -4, 0, 4, 0, -2, 7, -5, 0, -1, -1, 4, -2, 4, 0, 3, 0, -11, 16, -15, 19, -12, 0, 5, 2, -12, 0, 24, 0, -19, 12, -7, 0, -9, 23, -21, 0, 5, 0, 2, 2, -2, 14, -5, 0, -2, 0, 12, 9, -41, 32, 14, 0, -44, 58, -5, 0, -42, 0, 9, 5, 0, 75, -61, 0, -37, 9, -5, 0, 47, -48, 76, -5, -65, 0, 42, 42

Offset: 1

Author

Antti Karttunen, Apr 04 2020

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10200
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A332902, A333123.

Programs

Mathematica

Prepend[Differences[#], First[#]] &@ Nest[Append[#1, Sum[#1[[#2 - #2/p]], {p, FactorInteger[#2][[All, 1]]}]] & @@ {#, Length@ # + 1} &, {1}, 90] (* Michael De Vlieger, Apr 15 2020 *)

PARI

up_to = 105;
A333123list(up_to) = { my(v=vector(up_to)); v[1] = 1; for(n=2,up_to, v[n] = vecsum(apply(p -> v[n-n/p], factor(n)[, 1]~))); (v); };
v333123 = A333123list(up_to);
A333123(n) = v333123[n];
A332903(n) = if(1==n,n,(A333123(n)-A333123(n-1)));

Formula

a(1) = 1, and for n > 1, a(n) = A333123(n) - A333123(n-1).

a(p) = 0 for all primes p.