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 A320776 Inverse Euler transform of the number of prime factors (with multiplicity) function A001222. 7
 1, 0, 1, 1, 1, 0, -1, -1, 0, 1, 0, -1, -1, -1, 1, 3, 3, -2, -5, -4, 0, 7, 7, 0, -9, -10, 2, 15, 15, -3, -27, -30, 3, 46, 51, 1, -71, -91, -7, 117, 157, 23, -194, -265, -57, 318, 465, 111, -536, -821, -230, 893, 1456, 505, -1485, -2559, -1036, 2433, 4483, 2022 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,16 COMMENTS The Euler transform of a sequence q is the sequence of coefficients of x^n, n > 0, in the expansion of Product_{n > 0} 1/(1 - x^n)^q(n). The constant term 1 is sometimes taken to be the zeroth part of the Euler transform. LINKS Table of n, a(n) for n=0..59. MAPLE # The function EulerInvTransform is defined in A358451. a := EulerInvTransform(n -> ifelse(n=0, 1, NumberTheory:-NumberOfPrimeFactors(n))): seq(a(n), n = 0..59); # Peter Luschny, Nov 21 2022 MATHEMATICA EulerInvTransform[{}]={}; EulerInvTransform[seq_]:=Module[{final={}}, For[i=1, i<=Length[seq], i++, AppendTo[final, i*seq[[i]]-Sum[final[[d]]*seq[[i-d]], {d, i-1}]]]; Table[Sum[MoebiusMu[i/d]*final[[d]], {d, Divisors[i]}]/i, {i, Length[seq]}]]; EulerInvTransform[Array[PrimeOmega, 100]] CROSSREFS Number theoretical functions: A000005, A000010, A000203, A001055, A001221, A001222, A008683, A010054. Euler transforms: A000081, A001970, A006171, A007294, A061255, A061256, A061257, A073576, A117209, A293548, A293549. Inverse Euler transforms: A059966, A320767, A320777, A320778, A320779, A320780, A320781, A320782. Sequence in context: A116644 A166462 A328177 * A279056 A265751 A143050 Adjacent sequences: A320773 A320774 A320775 * A320777 A320778 A320779 KEYWORD sign AUTHOR Gus Wiseman, Oct 22 2018 STATUS approved

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Last modified November 29 06:17 EST 2023. Contains 367422 sequences. (Running on oeis4.)