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, 1, 3, 6, 12, 24, 48, 120, 264, 480, 1104, 2064, 4128, 10752, 19320, 38328, 91992, 170016, 369600, 745560, 1854720, 3845760, 7765296, 14990520, 29910120, 59856720, 119710416, 298755600, 667297320, 1446528360, 4011171840

Offset: 1

Author

Jaroslav Krizek, Sep 30 2009

Keywords

• nonn

Comments

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

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.

Examples

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

Programs

Mathematica

Module[{lst={1}},Do[AppendTo[lst,DivisorSigma[1,Total[lst]]],{40}]; lst] (* Harvey P. Dale, Sep 29 2012 *)

PARI

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

Extensions

Extension and program from Charles R Greathouse IV, Oct 12 2009