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A354352 Sum of primorial inflation (A108951) and its Dirichlet inverse.

%I A354352 #9 Jun 05 2022 23:20:17
%S A354352 2,0,0,4,0,24,0,8,36,120,0,24,0,840,360,16,0,72,0,120,2520,9240,0,48,
%T A354352 900,120120,216,840,0,0,0,32,27720,2042040,12600,144,0,38798760,
%U A354352 360360,240,0,0,0,9240,1080,892371480,0,96,44100,1800,6126120,120120,0,432,138600,1680,116396280,25878772920,0,720,0,802241960520
%N A354352 Sum of primorial inflation (A108951) and its Dirichlet inverse.
%H A354352 Antti Karttunen, <a href="/A354352/b354352.txt">Table of n, a(n) for n = 1..4710</a>
%H A354352 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A354352 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A354352 a(n) = A108951(n) + A354351(n).
%F A354352 a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A108951(d) * A354351(n/d).
%F A354352 For all n >= 1, a(A001248(n)) = A061742(n).
%o A354352 (PARI)
%o A354352 A002110(n) = prod(i=1,n,prime(i));
%o A354352 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) }; \\ From A108951
%o A354352 memoA354351 = Map();
%o A354352 A354351(n) = if(1==n,1,my(v); if(mapisdefined(memoA354351,n,&v), v, v = -sumdiv(n,d,if(d<n,A108951(n/d)*A354351(d),0)); mapput(memoA354351,n,v); (v)));
%o A354352 A354352(n) = (A354351(n)+A108951(n));
%Y A354352 Cf. A001248, A002110, A061742, A108951, A354351.
%K A354352 nonn
%O A354352 1,1
%A A354352 _Antti Karttunen_, Jun 05 2022