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 A361385 a(n) is the number of "Fermi-Dirac prime" factors (or I-components) of the n-th infinitary harmonic number. 1
 0, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 4, 3, 5, 5, 5, 4, 6, 5, 5, 6, 6, 5, 6, 5, 6, 6, 6, 5, 7, 4, 5, 5, 6, 7, 6, 6, 6, 7, 6, 6, 7, 6, 6, 6, 7, 6, 8, 7, 7, 7, 6, 7, 7, 7, 6, 8, 6, 5, 6, 7, 6, 7, 7, 6, 8, 7, 7, 8, 7, 6, 7, 8, 7, 6, 8, 7, 7, 7, 7, 9, 6, 8, 6, 8, 8, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Each term appears a finite number of times in the sequence (Hagis and Cohen, 1990). LINKS Amiram Eldar, Table of n, a(n) for n = 1..239 Peter Hagis, Jr. and Graeme L. Cohen, Infinitary harmonic numbers, Bull. Australian math. Soc., Vol. 41 (1990), pp. 151-158. FORMULA a(n) = A064547(A063947(n)). MATHEMATICA f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 2/(1 + p^(2^(m - j))), 1], {j, 1, m}]]; ih[1] = 1; ih[n_] := n*Times @@ f @@@ FactorInteger[n]; ic[n_] := Plus @@ (DigitCount[Last /@ FactorInteger[n], 2, 1]); ic[1] = 0; ic /@ Select[Range[10^5], IntegerQ[ih[#]] &] PROG (PARI) A064547(n) = {my(f = factor(n)[, 2]); sum(k=1, #f, hammingweight(f[k])); } \\ Michel Marcus at A064547 ihmean(n) = {my(f = factor(n), b); n * prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], 2/(f[i, 1]^(2^(#b-k))+1), 1))); }; lista(kmax) = {my(ih); for(k = 1, kmax, ih = ihmean(k); if(denominator(ih) == 1, print1(A064547(k), ", "))); } CROSSREFS Cf. A006086, A006087, A361384 (analogous unitary sequence). Sequence in context: A048686 A278959 A090501 * A126848 A232753 A067085 Adjacent sequences: A361382 A361383 A361384 * A361386 A361387 A361388 KEYWORD nonn AUTHOR Amiram Eldar, Mar 10 2023 STATUS approved

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Last modified August 15 03:46 EDT 2024. Contains 375172 sequences. (Running on oeis4.)