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Dirichlet inverse of A036288, where A036288(n) = 1 + sopfr(n), where sopfr is the sum of prime divisors with repetition, A001414.
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%I #8 Jan 17 2023 10:01:19

%S 1,-3,-4,4,-6,18,-8,-4,9,28,-12,-40,-14,38,39,4,-18,-63,-20,-64,53,58,

%T -24,64,25,68,-18,-88,-30,-253,-32,-4,81,88,83,216,-38,98,95,104,-42,

%U -347,-44,-136,-144,118,-48,-88,49,-175,123,-160,-54,180,127,144,137,148,-60,820,-62,158,-198,4,149,-535

%N Dirichlet inverse of A036288, where A036288(n) = 1 + sopfr(n), where sopfr is the sum of prime divisors with repetition, A001414.

%H Antti Karttunen, <a href="/A359789/b359789.txt">Table of n, a(n) for n = 1..16384</a>

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A036288(n/d) * a(d).

%o (PARI)

%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.

%o memoA359789 = Map();

%o A359789(n) = if(1==n,1,my(v); if(mapisdefined(memoA359789,n,&v), v, v = -sumdiv(n,d,if(d<n,(1+A001414(n/d))*A359789(d),0)); mapput(memoA359789,n,v); (v)));

%Y Cf. A001414, A036288, A359774 (parity of terms).

%Y Cf. also A359773, A359788, A359790, A359791.

%K sign

%O 1,2

%A _Antti Karttunen_, Jan 15 2023