A323247 a(n) = A005187(A156552(n)).

0, 1, 3, 4, 7, 8, 15, 11, 10, 16, 31, 19, 63, 32, 18, 26, 127, 23, 255, 35, 34, 64, 511, 42, 22, 128, 25, 67, 1023, 39, 2047, 57, 66, 256, 38, 50, 4095, 512, 130, 74, 8191, 71, 16383, 131, 41, 1024, 32767, 89, 46, 47, 258, 259, 65535, 54, 70, 138, 514, 2048, 131071, 82, 262143, 4096, 73, 120, 134, 135, 524287, 515

Offset: 1

Author

Antti Karttunen, Jan 10 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2048

Crossrefs

Cf. A001222, A005187, A006530, A156552, A252464, A253560, A323243, A323248.

Cf. also A283475.

Programs

PARI

A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
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))));
A323247(n) = A005187(A156552(n));

Formula

a(n) = A005187(A156552(n)).

a(n) = A323243(n) + A323248(n).

For n >= 2, a(A253560(n)) = a(n*A006530(n)) = a(n) + A000225(A001222(n)).

For n >= 1 and k >= 1, a(n*A000040(k+A000720(A006530(n)))) = a(n) + A000225(k+A001222(n)).