cp's OEIS Frontend

A359788 Dirichlet inverse of A075255, where A075255(n) = n - sopfr(n), where sopfr is the sum of prime factors (with repetition).

%I A359788 #8 Jan 16 2023 21:55:43
%S A359788 1,0,0,0,0,-1,0,-2,-3,-3,0,-5,0,-5,-7,-8,0,-10,0,-11,-11,-9,0,-15,-15,
%T A359788 -11,-18,-17,0,-20,0,-22,-19,-15,-23,-25,0,-17,-23,-29,0,-30,0,-29,
%U A359788 -34,-21,0,-33,-35,-38,-31,-35,0,-37,-39,-43,-35,-27,0,-42,0,-29,-50,-48,-47,-50,0,-47,-43,-56,0,-38,0,-35
%N A359788 Dirichlet inverse of A075255, where A075255(n) = n - sopfr(n), where sopfr is the sum of prime factors (with repetition).
%C A359788 The first positive term after a(1) occurs as a(144) = 13.
%H A359788 Antti Karttunen, <a href="/A359788/b359788.txt">Table of n, a(n) for n = 1..65537</a>
%F A359788 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A075255(n/d) * a(d).
%o A359788 (PARI)
%o A359788 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A359788 A075255(n) = (n-A001414(n));
%o A359788 memoA359788 = Map();
%o A359788 A359788(n) = if(1==n,1,my(v); if(mapisdefined(memoA359788,n,&v), v, v = -sumdiv(n,d,if(d<n,A075255(n/d)*A359788(d),0)); mapput(memoA359788,n,v); (v)));
%Y A359788 Cf. A001414, A075255, A359787 (parity of terms).
%Y A359788 Cf. also A359789.
%K A359788 sign
%O A359788 1,8
%A A359788 _Antti Karttunen_, Jan 15 2023