A322865 a(n) = A000265(A122111(n)).

1, 1, 1, 3, 1, 3, 1, 5, 9, 3, 1, 5, 1, 3, 9, 7, 1, 15, 1, 5, 9, 3, 1, 7, 27, 3, 25, 5, 1, 15, 1, 11, 9, 3, 27, 21, 1, 3, 9, 7, 1, 15, 1, 5, 25, 3, 1, 11, 81, 45, 9, 5, 1, 35, 27, 7, 9, 3, 1, 21, 1, 3, 25, 13, 27, 15, 1, 5, 9, 45, 1, 33, 1, 3, 75, 5, 81, 15, 1, 11, 49, 3, 1, 21, 27, 3, 9, 7, 1, 35, 81, 5, 9, 3, 27, 13, 1, 135, 25, 63, 1, 15, 1, 7, 75

Offset: 1

Author

Antti Karttunen, Dec 30 2018

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 binary expansion of n
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000265, A122111, A322813, A322819, A322820, A322826, A322865, A322867.

Programs

Mathematica

Array[#/2^IntegerExponent[#, 2] &@ If[# < 3, 1, 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] & @@@ FactorInteger@ #]] &, 105] (* Michael De Vlieger, Dec 31 2018, after JungHwan Min at A122111 *)

PARI

A000265(n) = (n>>valuation(n, 2));
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)));
A322865(n) = A000265(A122111(n));

Formula

a(n) = A000265(A122111(n)).

a(n) = A122111(A322820(n)).

A000005(a(n)) = A322813(n).

A000203(a(n)) = A322819(n).

A122111(a(n)) = A322820(n).

A000120(a(n)) = A322867(n).