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A324891
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a(n) = sigma(A170818(n)), where A170818(n) is the part of n composed of prime factors of form 4k+1.
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2
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1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 14, 1, 6, 1, 18, 1, 1, 6, 1, 1, 1, 1, 31, 14, 1, 1, 30, 6, 1, 1, 1, 18, 6, 1, 38, 1, 14, 6, 42, 1, 1, 1, 6, 1, 1, 1, 1, 31, 18, 14, 54, 1, 6, 1, 1, 30, 1, 6, 62, 1, 1, 1, 84, 1, 1, 18, 1, 6, 1, 1, 74, 38, 31, 1, 1, 14, 1, 6, 1, 42, 1, 1, 108, 1, 30, 1, 90, 6, 14, 1, 1, 1, 6, 1, 98, 1, 1, 31, 102, 18, 1, 14, 6
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OFFSET
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1,5
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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 == 1 (mod 4), otherwise a(p^e) = 1.
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PROG
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(PARI) A324891(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4>1, 1, ((f[i, 1]^(1+f[i, 2]))-1)/(f[i, 1]-1))); };
(PARI)
A170818(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4>1, 1, f[i, 1])^f[i, 2]); }; \\ From A170818
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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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