A081973 a(1) = 1; a(n) = a(n-1) + sigma(a(n-1)) where sigma(k) = sum of the divisors of k.

1, 2, 5, 11, 23, 47, 95, 215, 479, 959, 2063, 4127, 8255, 19007, 38327, 76655, 168647, 338663, 708263, 1453823, 3308543, 7154303, 14919599, 29910119, 59820239, 119676959, 239387375, 538142975, 1205440295, 2651968655, 6663140495

Offset: 1

Author

Amarnath Murthy, Apr 03 2003

Keywords

• nonn

Comments

a(n+1)/a(n) >= 2 for all n. Is a(n+1)/a(n) bounded? Up to n=160, the maximum value is a(31)/a(30)=2.5125261124174184479... - Benoit Cloitre, Apr 17 2003

a(n) == 23 (mod 24) for all n>=5. - Dean Hickerson, Apr 20 2003

a(n) = partial sums of A165929(n). [From Jaroslav Krizek, Sep 30 2009]

Links

• T. D. Noe, Table of n, a(n) for n=1..200

Programs

Mathematica

a[1]=1; a[n_] := a[n]=a[n-1]+DivisorSigma[1, a[n-1]]

Extensions

More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Apr 07 2003