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

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, 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, 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

Offset

1,4

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 computed from indices in prime factorization

Index entries for sequences related to Stern's sequences

Formula

a(n) = A002487(A331595(n)) = A002487(gcd(A122111(n), A241909(n))).

a(n) = A002487(A331731(n)).

Mathematica

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 *)

Prog

(PARI)
A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
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)};
A122111(n) = if(1==n, n, prime(bigomega(n))*A122111(A064989(n)));
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));
A331595(n) = gcd(A122111(n), A241909(n));
A331600(n) = A002487(A331595(n));

Crossrefs

Cf. A002487, A122111, A241909, A331595, A331731.

Cf. also A323901, A323902, A323903, A331601.

Sequence in context: A127669 A323436 A056692 * A039637 A194548 A274009

Adjacent sequences: A331597 A331598 A331599 * A331601 A331602 A331603

Keyword

nonn

Author

Antti Karttunen, Jan 22 2020

Status

approved