A297106 Xor-Moebius transform of A156552.

0, 1, 2, 2, 4, 6, 8, 4, 4, 12, 16, 12, 32, 24, 12, 8, 64, 12, 128, 24, 24, 48, 256, 24, 8, 96, 8, 48, 512, 20, 1024, 16, 48, 192, 24, 24, 2048, 384, 96, 48, 4096, 40, 8192, 96, 24, 768, 16384, 48, 16, 24, 192, 192, 32768, 24, 48, 96, 384, 1536, 65536, 40, 131072, 3072, 48, 32, 96, 80, 262144, 384, 768, 40, 524288, 48

Offset: 1

Author

Antti Karttunen, Dec 25 2017

Keywords

• nonn

Comments

Unique sequence satisfying SumXOR_{d divides n} a(d) = A156552(n) for all n > 0, where SumXOR is the analog of summation under the binary XOR operation. See A295901 for a list of some of the properties of the Xor-Moebius transform.

The ordinary Möbius transform of A156552 is given in A297112.

It seems that A091629 gives the fixed points of this sequence.

Links

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

Crossrefs

Cf. A064989, A091629, A156552, A295901, A297108, A297112.

Programs

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)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A297106(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A156552(d)))); (v); } \\ after code in A295901.