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A346103 Numerators of sequence whose Dirichlet convolution with itself yields A342920.

%I A346103 #11 Jul 12 2021 18:00:29
%S A346103 1,1,1,7,1,3,1,57,47,3,1,19,1,3,11,747,1,139,1,19,11,3,1,319,199,3,81,
%T A346103 19,1,231,1,-265,11,3,251,873,1,3,11,191,1,79,1,19,299,3,1,-157,5943,
%U A346103 595,11,19,1,151,187,31,11,3,1,269,1,3,507,-957,527,31,1,19,11,223,1,18787,1,3,8915,19,483,31,1,2147,19355
%N A346103 Numerators of sequence whose Dirichlet convolution with itself yields A342920.
%H A346103 Antti Karttunen, <a href="/A346103/b346103.txt">Table of n, a(n) for n = 1..10000</a>
%H A346103 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A346103 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A346103 (PARI)
%o A346103 up_to = 2310;
%o A346103 DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d<n, u[d]*u[n/d], 0)))/2); u}; \\ From A317937.
%o A346103 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A346103 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
%o A346103 A342002(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= p^(e>0); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
%o A346103 A342920(n) = A342002(A108951(n));
%o A346103 vA346103aux = DirSqrt(vector(up_to, n, A342920(n)));
%o A346103 A346103(n) = numerator(vA346103aux[n]);
%Y A346103 Cf. A046644 (gives the denominators).
%Y A346103 Cf. A108951, A324886, A342001, A342002, A342920, A346104.
%K A346103 sign,frac
%O A346103 1,4
%A A346103 _Antti Karttunen_, Jul 09 2021