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

Author

Antti Karttunen, Dec 01 2017

Keywords

• sign

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A033879, A286449.

Programs

PARI

A033879(n) = ((2*n)-sigma(n));
A293438(n) = { my(m=1); fordiv(n,d,if(dA033879(d))); (m); };

Formula

a(n) = Product_{d|n, dA033879(d).

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