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A165929 a(1) = 1; for n > 1, a(n) = sigma(sum of the previous terms) where sigma(k) = sum of the divisors of k. 1

%I #11 Oct 02 2023 20:17:29

%S 1,1,3,6,12,24,48,120,264,480,1104,2064,4128,10752,19320,38328,91992,

%T 170016,369600,745560,1854720,3845760,7765296,14990520,29910120,

%U 59856720,119710416,298755600,667297320,1446528360,4011171840

%N a(1) = 1; for n > 1, a(n) = sigma(sum of the previous terms) where sigma(k) = sum of the divisors of k.

%C a(1) = 1; for n > 1, a(n) = sigma(Sum_{i=1..n-1} a(i)) = A000203(Sum_{i=1..n-1} a(i)).

%C a(n) = inverse of partial sums of A081973(n), i.e., a(1) = A081973(1); for n > 1, a(n) = A081973(n) - A081973(n-1), i.e., first differences of A081973.

%e a(4) = sigma(a(1) + a(2) + a(3)) = sigma(1+1+3) = sigma(5) = 6.

%t Module[{lst={1}},Do[AppendTo[lst,DivisorSigma[1,Total[lst]]],{40}]; lst] (* _Harvey P. Dale_, Sep 29 2012 *)

%o (PARI) print1(1);s=1;for(i=1,100,k=sigma(s);print1(","k);s+=k)

%K nonn

%O 1,3

%A _Jaroslav Krizek_, Sep 30 2009

%E Extension and program from _Charles R Greathouse IV_, Oct 12 2009

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)