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 A224892 Dirichlet g.f.: Product_{k>=2} (1 - 1/k^(s-1)). 4
 1, -2, -3, -4, -5, 0, -7, 0, -9, 0, -11, 12, -13, 0, 0, 0, -17, 18, -19, 20, 0, 0, -23, 24, -25, 0, 0, 28, -29, 30, -31, 32, 0, 0, 0, 36, -37, 0, 0, 40, -41, 42, -43, 44, 45, 0, -47, 48, -49, 50, 0, 52, -53, 54, 0, 56, 0, 0, -59, 60, -61, 0, 63, 0, 0, 66, -67, 68, 0, 70, -71, 72, -73, 0, 75, 76, 0, 78, -79, 80, 0, 0, -83, 84, 0, 0, 0, 88, -89, 90 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Old name (which appeared to be incorrect) was "a(1)=1; for n>1, let n = p_1^e_1*p_2^e_2*...*p_k^e_k be the prime factorization of n; then a(n) = -n if k=1 and e_1 is 1 or 2; a(n) = +n if k=2 and e1, e_2 are not both 1; a(n) = -n if k >= 3; and a(n) = 0 otherwise." Every factor (1 - 1/n^(s-1)) corresponds to an operator whose row sums are the numerators in the Dirichlet series that converges to log(n). LINKS Michael De Vlieger, Table of n, a(n) for n = 1..512 FORMULA Dirichlet g.f.: Product_{k>=2} (1 - 1/k^(s-1)). MATHEMATICA Clear[nn, logarithm, LOGPRODUCT, LOGi, n, k]; nn = 90; logarithm = 1; LOGPRODUCT = Table[Table[If[n/k == logarithm, n/k, If[n == k, 1, 0]], {k, 1, nn}], {n, 1, nn}]; Monitor[Do[logarithm = i; LOGi = Table[Table[If[n/k == logarithm, -n/k, If[n == k, 1, 0]], {k, 1, nn}], {n, 1, nn}]; LOGPRODUCT = LOGPRODUCT.LOGi; , {i, 2, nn}], i]; LOGPRODUCT[[All, 1]] PROG (PARI) seq(n)={my(v=vector(n, k, k==1)); for(k=2, n, my(w=vector(n)); w[1]=1; w[k]=-k; v=dirmul(v, w)); v} \\ Andrew Howroyd, Dec 31 2019 CROSSREFS Sequence in context: A279385 A267000 A365430 * A351233 A265517 A063972 Adjacent sequences: A224889 A224890 A224891 * A224893 A224894 A224895 KEYWORD sign AUTHOR Mats Granvik, Jul 24 2013 EXTENSIONS Definition edited by N. J. A. Sloane, Apr 24 2017 New name from Jon E. Schoenfield, Jan 06 2020 STATUS approved

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Last modified February 21 13:52 EST 2024. Contains 370235 sequences. (Running on oeis4.)