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1, -1, -2, -10, -1, 2, -2, 18, -25, 1, -5, 20, -4, 2, 2, 46, -3, 25, -2, 10, 4, 5, -6, -36, -33, 4, 86, 20, -1, -2, -17, -220, 10, 3, 2, 250, -10, 2, 8, -18, -7, -4, -2, 50, 25, 6, -8, -92, -81, 33, 6, 40, -6, -86, 5, -36, 4, 1, -29, -20, -13, 17, 50, -886, 4, -10, -4, 30, 12, -2, -31, -450, -3, 10, 66, 20, 10, -8, -10
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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a(1) = 1; a(n) = -Sum_{d|n, d < n} A326042(n/d) * a(d).
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MATHEMATICA
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f1[p_, e_] := NextPrime[p]^e; s1[1] = 1; s1[n_] := Times @@ f1 @@@ FactorInteger[n]; f2[2, e_] := 1; f2[p_, e_] := NextPrime[p, -1]^e; s2[1] = 1; s2[n_] := Times @@ f2 @@@ FactorInteger[n]; s[n_] := s2[DivisorSigma[1, s1[n]]]; a[1] = 1; a[n_] := a[n] = -DivisorSum[n, a[#]*s[n/#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Nov 27 2021 *)
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PROG
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(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
memoA349623 = Map();
A349623(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349623, n, &v), v, v = -sumdiv(n, d, if(d<n, A326042(n/d)*A349623(d), 0)); mapput(memoA349623, n, v); (v)));
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CROSSREFS
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KEYWORD
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sign,mult
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AUTHOR
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STATUS
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approved
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