A081973 - OEIS

A081973

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

%I #24 Feb 23 2024 07:26:14

%S 1,2,5,11,23,47,95,215,479,959,2063,4127,8255,19007,38327,76655,

%T 168647,338663,708263,1453823,3308543,7154303,14919599,29910119,

%U 59820239,119676959,239387375,538142975,1205440295,2651968655,6663140495

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

%C 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

%C a(n) == 23 (mod 24) for all n>=5. - _Dean Hickerson_, Apr 20 2003

%C a(n) = partial sums of A165929(n). [From _Jaroslav Krizek_, Sep 30 2009]

%H T. D. Noe, <a href="/A081973/b081973.txt">Table of n, a(n) for n=1..200</a>

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

%K nonn

%O 1,2

%A _Amarnath Murthy_, Apr 03 2003

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