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

1,3

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

Prog

(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.

Crossrefs

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

Sequence in context: A178702 A265992 A089284 * A357877 A299925 A350652

Adjacent sequences: A297103 A297104 A297105 * A297107 A297108 A297109

Keyword

nonn

Author

Antti Karttunen, Dec 25 2017

Status

approved