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1, 0, 0, 1, -1, 2, -1, 4, 4, 3, -4, 4, -4, 5, 6, 13, -7, 6, -7, 5, 10, 6, -8, 10, 5, 8, 24, 9, -13, -2, -12, 40, 12, 9, 16, 16, -16, 11, 16, 11, -19, -2, -19, 8, 14, 14, -20, 28, 19, 9, 18, 12, -23, 26, 22, 21, 22, 15, -28, 2, -27, 18, 26, 121, 28, -8, -31, 11, 28, -8, -34, 46, -33, 20, 18, 15, 34, -8, -37, 29, 124
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,6
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COMMENTS
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LINKS
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FORMULA
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MATHEMATICA
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f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := (1 + Times @@ f @@@ FactorInteger[n])/2; a[n_] := DivisorSum[n, # * MoebiusMu[#] * s[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 23 2021 *)
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PROG
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(PARI)
A048673(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1/2)*(1+factorback(f)); };
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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