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A324893
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a(n) = sigma(A097706(n)), where A097706(n) is the part of n composed of prime factors of form 4k+3.
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2
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1, 1, 4, 1, 1, 4, 8, 1, 13, 1, 12, 4, 1, 8, 4, 1, 1, 13, 20, 1, 32, 12, 24, 4, 1, 1, 40, 8, 1, 4, 32, 1, 48, 1, 8, 13, 1, 20, 4, 1, 1, 32, 44, 12, 13, 24, 48, 4, 57, 1, 4, 1, 1, 40, 12, 8, 80, 1, 60, 4, 1, 32, 104, 1, 1, 48, 68, 1, 96, 8, 72, 13, 1, 1, 4, 20, 96, 4, 80, 1, 121, 1, 84, 32, 1, 44, 4, 12, 1, 13, 8, 24, 128, 48, 20, 4, 1, 57, 156, 1, 1, 4
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OFFSET
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1,3
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LINKS
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FORMULA
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Multiplicative with a(p^e) = (p^(e+1) - 1)/(p-1) if p == 3 (mod 4), otherwise a(p^e) = 1.
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MATHEMATICA
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Array[DivisorSigma[1, Times @@ Power @@@ Select[FactorInteger[#], Mod[#[[1]], 4] == 3 &]] &, 102] (* Michael De Vlieger, Mar 30 2019 *)
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PROG
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(PARI) A324893(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4<3, 1, ((f[i, 1]^(1+f[i, 2]))-1)/(f[i, 1]-1))); };
(PARI)
A097706(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4<3, 1, f[i, 1])^f[i, 2]); };
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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