A322993 a(1) = 0; for n > 1, a(n) = A000265(A156552(n)).

0, 1, 1, 3, 1, 5, 1, 7, 3, 9, 1, 11, 1, 17, 5, 15, 1, 13, 1, 19, 9, 33, 1, 23, 3, 65, 7, 35, 1, 21, 1, 31, 17, 129, 5, 27, 1, 257, 33, 39, 1, 37, 1, 67, 11, 513, 1, 47, 3, 25, 65, 131, 1, 29, 9, 71, 129, 1025, 1, 43, 1, 2049, 19, 63, 17, 69, 1, 259, 257, 41, 1, 55, 1, 4097, 13, 515, 5, 133, 1, 79, 15, 8193, 1, 75, 33, 16385, 513, 135, 1, 45, 9

Offset: 1

Author

Antti Karttunen, Jan 02 2019

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192

Crossrefs

Cf. A000265, A156552, A246277, A305897 (restricted growth sequence transform), A322994 (Möbius transform).

Cf. also A322995.

Programs

Mathematica

Array[#/2^IntegerExponent[#, 2] &@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ #]] &, 91] (* Michael De Vlieger, Jan 03 2019 *)

PARI

A000265(n) = (n/2^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)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A322993(n) = if(1==n,0,A000265(A156552(n)));

Formula

a(1) = 0; for n > 1, a(n) = A000265(A156552(n)).

For n > 1, a(n) = A156552(2*A246277(n)).

A000120(a(n)) = A001222(n) for all n >= 1.