A361385 a(n) is the number of "Fermi-Dirac prime" factors (or I-components) of the n-th infinitary harmonic number.
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
Offset: 1
Keywords
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.
Programs
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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[#]] &] -
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), ", ")));}
Comments