A336125 a(n) = A292385(A122111(n)).

0, 1, 2, 2, 4, 4, 8, 5, 5, 8, 16, 10, 32, 16, 10, 10, 64, 8, 128, 20, 20, 32, 256, 20, 8, 64, 11, 40, 512, 16, 1024, 20, 40, 128, 16, 21, 2048, 256, 80, 40, 4096, 32, 8192, 80, 22, 512, 16384, 40, 17, 17, 160, 160, 32768, 16, 32, 80, 320, 1024, 65536, 42, 131072, 2048, 44, 41, 64, 64, 262144, 320, 640, 34, 524288, 41, 1048576, 4096, 20

Offset: 1

Author

Antti Karttunen, Jul 17 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A064989, A122111, A253553, A253566, A292385, A336120, A336123, A336313.

Programs

PARI

\\ Uses also code given in A336124:
A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
A336125(n) = if(n<=2,n-1,(1==A336124(n))+(2*A336125(A253553(n))));

PARI

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)));
A252463(n) = if(!(n%2),n/2,A064989(n));
A292385(n) = if(n<=2,n-1,(1==(n%4))+(2*A292385(A252463(n))));
A336125(n) = A292385(A122111(n));

Formula

a(1) = 0, a(2) = 1, and for n > 2, a(n) = [A122111(n) == 1 (mod 4)] + 2*a(A253553(n)).

a(n) = A292385(A122111(n)).

a(n) = A253566(n) - A336120(n).

A000120(a(n)) = A336123(n).