A324294 a(n) = A002487(1+sigma(n)).

1, 1, 3, 1, 3, 5, 4, 1, 3, 7, 5, 7, 4, 7, 7, 1, 7, 3, 8, 13, 6, 11, 7, 9, 1, 13, 11, 10, 5, 15, 6, 1, 9, 11, 9, 7, 10, 9, 10, 19, 13, 11, 12, 21, 13, 15, 9, 11, 7, 9, 15, 16, 11, 13, 15, 13, 14, 19, 9, 29, 6, 11, 18, 1, 21, 19, 14, 7, 11, 19, 15, 9, 18, 17, 11, 22, 11, 29, 14, 25, 9, 7, 21, 16, 19, 17, 13, 31, 19, 29, 13, 29, 8, 19, 13, 13, 16

Offset: 1

Author

Antti Karttunen, Feb 22 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to sigma(n)
• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A000203, A002487, A324288, A324293.

Programs

Mathematica

A002487[m_] := Module[{a = 1, b = 0, n = m}, While[n > 0, If[OddQ[n], b = a + b, a = a + b]; n = Floor[n/2]]; b];
a[n_] := A002487[1 + DivisorSigma[1, n]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 11 2023 *)

PARI

A002487(n) = { my(s=sign(n), a=1, b=0); n = abs(n); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (s*b); };
A324294(n) = A002487(1+sigma(n));

Python

from functools import reduce
from sympy import divisor_sigma
def A324294(n): return reduce(lambda x,y:(x[0],x[0]+x[1]) if int(y) else (x[0]+x[1],x[1]),bin(divisor_sigma(n)+1)[-1:1:-1],(1,0))[1] # Chai Wah Wu, Jun 19 2022

Formula

a(n) = A002487(1+sigma(n)).

a(2^n) = 1 for all n >= 0, but also for some other numbers, e.g., a(25) = 1.