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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 (list; graph; refs; listen; history; text; internal format)
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_{d|n, d<n} (1-A000035(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

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Last modified November 22 03:35 EST 2019. Contains 329386 sequences. (Running on oeis4.)