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A002750 Sum of logarithmic numbers.

%I A002750 M3506 N1422 #33 Nov 19 2024 10:35:16
%S A002750 1,4,15,76,373,2676,17539,152860,1383561,14658148,143131351,
%T A002750 2070738924,24754959805,341745565396,5260157782923,92358395065276,
%U A002750 1377499388715409,27622124789948100,476285499100204831,10464946811144407948,222724531608924013701
%N A002750 Sum of logarithmic numbers.
%D A002750 J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83.
%D A002750 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002750 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002750 Robert Israel, <a href="/A002750/b002750.txt">Table of n, a(n) for n = 0..447</a>
%H A002750 J. M. Gandhi, <a href="/A002741/a002741.pdf">On logarithmic numbers</a>, Math. Student, 31 (1963), 73-83. [Annotated scanned copy]
%H A002750 <a href="/index/Lo#logarithmic">Index entries for sequences related to logarithmic numbers</a>
%F A002750 E.g.f.: F(x)/x*exp(x) where F(x) is o.g.f. for A000203(). a(n) = Sum_{m=1..n+1} A000203(m)*binomial(n, m-1)*(m-1)!. - _Vladeta Jovovic_, Feb 08 2003
%p A002750 a:= n-> n!*add(numtheory[sigma](m+1)/(n-m)!, m=0..n):
%p A002750 seq(a(n), n=0..22);  # _Alois P. Heinz_, Sep 16 2021
%t A002750 a[n_] := n!*Sum[DivisorSigma[1, m+1]/(n-m)!, {m, 0, n}];
%t A002750 Table[a[n], {n, 0, 22}] (* _Jean-François Alcover_, Nov 19 2024, after _Alois P. Heinz_ *)
%Y A002750 Cf. A000203.
%K A002750 nonn
%O A002750 0,2
%A A002750 _N. J. A. Sloane_
%E A002750 More terms from _Jeffrey Shallit_
%E A002750 More terms from _Vladeta Jovovic_, Feb 08 2003