cp's OEIS Frontend

A331600 a(n) = A002487(A331595(n)).

%I A331600 #15 Jan 26 2020 20:56:12
%S A331600 1,1,1,2,1,2,1,3,2,2,1,3,1,2,4,3,1,4,1,3,4,2,1,3,2,2,3,3,1,4,1,5,4,2,
%T A331600 4,3,1,2,4,3,1,4,1,3,7,2,1,5,2,12,4,3,1,3,8,3,4,2,1,3,1,2,7,5,8,4,1,3,
%U A331600 4,12,1,5,1,2,4,3,4,4,1,5,3,2,1,3,8,2,4,3,1,3,8,3,4,2,8,5,1,16,7,3,1,4,1,3,18
%N A331600 a(n) = A002487(A331595(n)).
%H A331600 Antti Karttunen, <a href="/A331600/b331600.txt">Table of n, a(n) for n = 1..16384</a>
%H A331600 Antti Karttunen, <a href="/A331600/a331600.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A331600 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A331600 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A331600 a(n) = A002487(A331595(n)) = A002487(gcd(A122111(n), A241909(n))).
%F A331600 a(n) = A002487(A331731(n)).
%t A331600 Array[If[# == 1, 1, NestWhile[If[OddQ[#3], {#1, #1 + #2, #4}, {#1 + #2, #2, #4}] & @@ Append[#, Floor[#[[-1]]/2]] &, {1, 0, #}, #[[-1]] > 0 &][[2]] &@ Apply[GCD, {Block[{k = #, m = 0}, Times @@ Power @@@ Table[k -= m; k = DeleteCases[k, 0]; {Prime@ Length@ k, m = Min@ k}, Length@ Union@ k]] &@ Catenate[ConstantArray[PrimePi[#1], #2] & @@@ #], Function[t, Times @@ Prime@ Accumulate[If[Length@ t < 2, {0}, Join[{1}, ConstantArray[0, Length@ t - 2], {-1}]] + ReplacePart[t, Map[#1 -> #2 & @@ # &, #]]]]@ ConstantArray[0, Transpose[#][[1, -1]]] &[# /. {p_, e_} /; p > 0 :> {PrimePi@ p, e}]}] &@ FactorInteger[#]] &, 105] (* _Michael De Vlieger_, Jan 25 2020, after _JungHwan Min_ at A122111 *)
%o A331600 (PARI)
%o A331600 A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
%o A331600 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A331600 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A331600 A241909(n) = if(1==n||isprime(n),2^primepi(n),my(f=factor(n),h=1,i,m=1,p=1,k=1); while(k<=#f~, p = nextprime(1+p); i = primepi(f[k,1]); m *= p^(i-h); h = i; if(f[k,2]>1, f[k,2]--, k++)); (p*m));
%o A331600 A331595(n) = gcd(A122111(n), A241909(n));
%o A331600 A331600(n) = A002487(A331595(n));
%Y A331600 Cf. A002487, A122111, A241909, A331595, A331731.
%Y A331600 Cf. also A323901, A323902, A323903, A331601.
%K A331600 nonn
%O A331600 1,4
%A A331600 _Antti Karttunen_, Jan 22 2020