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%I #14 Mar 11 2023 08:00:35
%S 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,
%T 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,
%U 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
%N a(n) = A002487(1+sigma(n)).
%H Antti Karttunen, <a href="/A324294/b324294.txt">Table of n, a(n) for n = 1..16384</a>
%H Antti Karttunen, <a href="/A324294/a324294.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F a(n) = A002487(1+sigma(n)).
%F a(2^n) = 1 for all n >= 0, but also for some other numbers, e.g., a(25) = 1.
%t 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];
%t a[n_] := A002487[1 + DivisorSigma[1, n]];
%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Mar 11 2023 *)
%o (PARI)
%o 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); };
%o A324294(n) = A002487(1+sigma(n));
%o (Python)
%o from functools import reduce
%o from sympy import divisor_sigma
%o 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
%Y Cf. A000203, A002487, A324288, A324293.
%K nonn
%O 1,3
%A _Antti Karttunen_, Feb 22 2019
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