A293438 Product of deficiencies of proper divisors of n.

1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 0, 1, 6, 8, 1, 1, 0, 1, 8, 12, 10, 1, 0, 4, 12, 10, 24, 1, 0, 1, 1, 20, 16, 24, 0, 1, 18, 24, -16, 1, 0, 1, 80, 240, 22, 1, 0, 6, 152, 32, 120, 1, 0, 40, 0, 36, 28, 1, 0, 1, 30, 600, 1, 48, 0, 1, 224, 44, 4224, 1, 0, 1, 36, 912, 288, 60, 0, 1, 160, 140, 40, 1, 0, 64, 42, 56, 320, 1, 0, 72, 440, 60, 46, 72

Offset

1,6

Comments

There are only 643 negative values in range 1 .. 16384.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = Product_{d|n, d<n} A033879(d).

a(A000040(n)) = 1, a(A000079(n)) = 1.

Example

The proper divisors of 15 are 1, 3, 5. Their deficiencies (A033879) are 1, 2, 4. Thus a(15) = 1*2*4 = 8.
The proper divisors of 18 are 1, 2, 3, 6, 9. Their deficiencies are 1, 1, 2, 0, 5, thus a(18) = 1*1*2*0*5 = 0.
The proper divisors of 40 are 1, 2, 4, 5, 8, 10, 20. Their deficiencies are 1, 1, 1, 4, 1, 2, -2, thus a(40) = 1 * 1 * 1 * 4 * 1 * 2 * -2 = -16.

Prog

(PARI)
A033879(n) = ((2*n)-sigma(n));
A293438(n) = { my(m=1); fordiv(n, d, if(d<n, m *= A033879(d))); (m); };

Crossrefs

Cf. A033879, A286449.

Sequence in context: A166918 A143576 A297159 * A318622 A353785 A245195

Adjacent sequences: A293435 A293436 A293437 * A293439 A293440 A293441

Keyword

sign

Author

Antti Karttunen, Dec 01 2017

Status

approved