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 A349910 a(n) = Sum_{d|n, d
 0, 1, 1, 3, 1, 6, 1, 8, 4, 7, 1, 19, 1, 9, 8, 22, 1, 27, 1, 23, 10, 10, 1, 56, 5, 12, 17, 31, 1, 47, 1, 63, 11, 13, 11, 93, 1, 15, 13, 69, 1, 65, 1, 35, 39, 18, 1, 165, 7, 43, 14, 43, 1, 128, 12, 95, 16, 19, 1, 160, 1, 22, 51, 185, 14, 74, 1, 47, 19, 80, 1, 288, 1, 24, 51, 55, 14, 92, 1, 205, 80, 25, 1, 226, 15, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Antti Karttunen, Table of n, a(n) for n = 1..20000 FORMULA a(n) = A336840(n) - A048673(n). MATHEMATICA f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := (1 + Times @@ f @@@ FactorInteger[n])/2; a[n_] := DivisorSum[n, s[#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Dec 12 2021 *) PROG (PARI) A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; }; A349910(n) = sumdiv(n, d, if(d==n, 0, A048673(d))); CROSSREFS Cf. A048673, A336840. Sequence in context: A336646 A336647 A336645 * A168111 A309491 A109646 Adjacent sequences:  A349907 A349908 A349909 * A349911 A349912 A349913 KEYWORD nonn AUTHOR Antti Karttunen, Dec 10 2021 STATUS approved

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Last modified August 11 22:58 EDT 2022. Contains 356067 sequences. (Running on oeis4.)