A287093 a(0) = 0, a(1) = 2; a(2*n) = sopf(a(n)), a(2*n+1) = a(n) + a(n+1), where sopf() is the sum of the distinct prime factors (A008472).

0, 2, 2, 4, 2, 6, 2, 6, 2, 8, 5, 8, 2, 8, 5, 8, 2, 10, 2, 13, 5, 13, 2, 10, 2, 10, 2, 13, 5, 13, 2, 10, 2, 12, 7, 12, 2, 15, 13, 18, 5, 18, 13, 15, 2, 12, 7, 12, 2, 12, 7, 12, 2, 15, 13, 18, 5, 18, 13, 15, 2, 12, 7, 12, 2, 14, 5, 19, 7, 19, 5, 14, 2, 17, 8, 28, 13, 31, 5, 23, 5, 23, 5, 31, 13, 28, 8, 17, 2, 14, 5

Offset

0,2

Comments

A variation on Stern's diatomic sequence.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Michael Gilleland, Some Self-Similar Integer Sequences

Ilya Gutkovskiy, Extended graphical example

Eric Weisstein's World of Mathematics, Stern's Diatomic Series

Index entries for sequences related to Stern's sequences

Example

a(0) = 0;
a(1) = 2;
a(2) = a(2*1) = sopf(a(1)) = 2;
a(3) = a(2*1+1) = a(1) + a(2) = 4;
a(4) = a(2*2) = sopf(a(2)) = 2;
a(5) = a(2*2+1) = a(2) + a(3) = 6;
a(6) = a(2*3) = sopf(a(3)) = 2, etc.

Mathematica

a[0] = 0; a[1] = 2; a[n_] := If[EvenQ[n], DivisorSum[a[n/2], # &, PrimeQ[#] &], a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 90}]

Prog

(PARI) a(n) = if (n==0, 0, if (n ==1, 2, if (n%2, a((n-1)/2) + a((n+1)/2), vecsum(factor(a(n/2))[, 1])))); \\ Michel Marcus, Dec 17 2017

Crossrefs

Cf. A002487, A008472, A287051.

Sequence in context: A323407 A354875 A073348 * A122457 A319410 A337174

Adjacent sequences: A287090 A287091 A287092 * A287094 A287095 A287096

Keyword

nonn,look

Author

Ilya Gutkovskiy, May 19 2017

Status

approved