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A319684
Sum of A003415(d) over the divisors d of n, where A003415 is arithmetic derivative.
12
0, 1, 1, 5, 1, 7, 1, 17, 7, 9, 1, 27, 1, 11, 10, 49, 1, 34, 1, 37, 12, 15, 1, 83, 11, 17, 34, 47, 1, 54, 1, 129, 16, 21, 14, 114, 1, 23, 18, 117, 1, 68, 1, 67, 55, 27, 1, 227, 15, 64, 22, 77, 1, 142, 18, 151, 24, 33, 1, 190, 1, 35, 69, 321, 20, 96, 1, 97, 28, 90, 1, 326, 1, 41, 75, 107, 20, 110, 1, 325, 142, 45, 1, 244, 24, 47, 34, 219, 1, 243, 22
OFFSET
1,4
COMMENTS
Inverse Möbius transform of A003415.
LINKS
FORMULA
a(n) = Sum_{d|n} A003415(d).
a(n) = A319683(n) + A003415(n).
MATHEMATICA
Block[{a}, a[1] = 0; a[n_] := a[n] = If[n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[n]]]; Array[DivisorSum[#, a[#] &] &, 91]] (* Michael De Vlieger, May 24 2021 *)
PROG
(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A319684(n) = sumdiv(n, d, A003415(d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 02 2018
STATUS
approved