A283764 a(0) = 0; a(1) = 1; a(2*n) = sigma(a(n)), a(2*n+1) = sigma(a(n)+a(n+1)).

0, 1, 1, 3, 1, 7, 4, 7, 1, 15, 8, 12, 7, 12, 8, 15, 1, 31, 24, 24, 15, 42, 28, 20, 8, 20, 28, 42, 15, 24, 24, 31, 1, 63, 32, 72, 60, 124, 60, 56, 24, 80, 96, 144, 56, 124, 42, 56, 15, 56, 42, 124, 56, 144, 96, 80, 24, 56, 60, 124, 60, 72, 32, 63, 1, 127, 104, 120, 63, 210, 195, 336, 168, 360, 224, 360, 168, 210, 120, 186, 60, 210, 186, 372, 252, 744, 403, 465, 120, 546

Offset: 0

Author

Ilya Gutkovskiy, Mar 16 2017

Keywords

• nonn

Comments

A variation on Stern's diatomic sequence (A002487) and iterating the sum of the divisors function (A007497).

Links

• Michael Gilleland, Some Self-Similar Integer Sequences
• Ilya Gutkovskiy, Extended graphical example
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A002487, A007497, A283166.

Programs

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], DivisorSigma[1, a[n/2]], DivisorSigma[1, a[(n - 1)/2] + a[(n + 1)/2]]]; Table[a[n], {n, 0, 100}]

PARI

a(n) = if(n<2, n, if(Mod(n,2), sigma(a((n - 1)/2) + a((n + 1)/2)), sigma(a(n/2))));
for(n=0, 100, print1(a(n),", ")) \\ Indranil Ghosh, Mar 16 2017