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, 15858104975, 36398968847, 72800044727

Offset

1,2

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

Partial sums of A165929. - Jaroslav Krizek, Sep 30 2009

Links

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

Mathematica

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

Prog

(PARI) lista(nn) = my(va=vector(nn)); va[1] = 1; for (n=2, nn, va[n] = va[n-1]+sigma(va[n-1])); va; \\ Michel Marcus, May 22 2026

Crossrefs

Cf. A000203, A165929.

Sequence in context: A083329 A055010 A266550 * A357292 A334276 A055496

Adjacent sequences: A081970 A081971 A081972 * A081974 A081975 A081976

Keyword

nonn

Author

Amarnath Murthy, Apr 03 2003

Extensions

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

Status

approved