

A320003


Number of proper divisors of n of the form 6*k + 3.


5



0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 1, 0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1, 0, 0, 4, 0, 0, 1, 0, 0, 1, 0, 0, 3, 0, 0, 2, 0, 0, 3
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OFFSET

1,18


COMMENTS

Number of divisors of n that are odd multiples of 3 and less than n.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537


FORMULA

a(n) = Sum_{dn, d<n} (1A000035(d))*A079978(d).
a(n) = A007814(A319990(n)).
a(4*n) = a(2*n).  David A. Corneth, Oct 03 2018


EXAMPLE

For n = 18, of its five proper divisors [1, 2, 3, 6, 9] only 3 and 9 are odd multiples of three, thus a(18) = 2.
For n = 108, the odd part is 27 for which 27/3 has 3 divisors. As 108 is even, we don't subtract 1 from that 3 to get a(108) = 3.  David A. Corneth, Oct 03 2018


PROG

(PARI) A320003(n) = if(!n, n, sumdiv(n, d, (d<n)*(3==(d%6))));
(PARI) a(n) = if(n%3==0, my(v=valuation(n, 2)); n>>=v; numdiv(n/3)(!v), 0) \\ David A. Corneth, Oct 03 2018


CROSSREFS

Cf. A319990, A320001, A320005.
Sequence in context: A016232 A007949 A191265 * A291749 A253786 A078595
Adjacent sequences: A320000 A320001 A320002 * A320004 A320005 A320006


KEYWORD

nonn,easy


AUTHOR

Antti Karttunen, Oct 03 2018


STATUS

approved



