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URL: https://oeis.org/A293438

⇱ A293438 - OEIS

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A293438
Product of deficiencies of proper divisors of n.
2
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
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
Sequence in context: A166918 A143576 A297159 * A318622 A353785 A245195
KEYWORD
sign
AUTHOR
Antti Karttunen, Dec 01 2017
STATUS
approved