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A324811 a(n) = A324728(n) - A061395(n). 2
0, 0, 0, 2, 0, 1, 0, 3, 2, 1, 0, 2, 0, 1, 2, 4, 0, 1, 0, 2, 2, 1, 0, 3, 2, 1, 3, 2, 0, 3, 0, 5, 1, 1, 2, 4, 0, 1, 2, 3, 0, 1, 0, 2, 3, 1, 0, 4, 2, 1, 1, 2, 0, 1, 2, 3, 2, 1, 0, 2, 0, 1, 1, 6, 1, 2, 0, 2, 1, 1, 0, 5, 0, 1, 3, 2, 2, 1, 0, 4, 5, 1, 0, 3, 2, 1, 2, 3, 0, 4, 2, 2, 1, 1, 2, 5, 0, 1, 3, 4, 0, 2, 0, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The first negative term is a(182) = -6, as A324712(182) = 0 and 182 = 2*7*13 = prime(1) * prime(4) * prime(6).

The next negative term after that is a(198) = -4, as A324712(198) = 1, and 198 = 2 * 3^2 * 11 = prime(1) * prime(2)^2 * prime(5).

There are only 161 negative terms among the first 10000 terms.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)

Index entries for sequences related to binary expansion of n

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

FORMULA

a(n) = A324728(n) - A061395(n).

a(p) = 0 for all primes p.

PROG

(PARI)

A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));

A324712(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A323243(d)))); (v); }; \\ Needs also code from A323243.

A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523

A324728(n) = { my(k=A324712(n)); if(!k, k, (1+A000523(k))); };

A324811(n) = (A324728(n) - A061395(n));

CROSSREFS

Cf. A000523, A061395, A323243, A324712, A324728.

Sequence in context: A187496 A193056 A244417 * A086780 A158612 A143782

Adjacent sequences:  A324808 A324809 A324810 * A324812 A324813 A324814

KEYWORD

sign

AUTHOR

Antti Karttunen, Mar 17 2019

STATUS

approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)