

A296074


Sum of deficiencies of the proper divisors of n.


6



0, 1, 1, 2, 1, 4, 1, 3, 3, 6, 1, 5, 1, 8, 7, 4, 1, 9, 1, 9, 9, 12, 1, 2, 5, 14, 8, 13, 1, 16, 1, 5, 13, 18, 11, 3, 1, 20, 15, 8, 1, 24, 1, 21, 18, 24, 1, 9, 7, 27, 19, 25, 1, 20, 15, 14, 21, 30, 1, 1, 1, 32, 24, 6, 17, 40, 1, 33, 25, 40, 1, 27, 1, 38, 32, 37, 17, 48, 1, 1, 22, 42, 1, 9, 21, 44, 31, 26, 1, 18, 19, 45, 33, 48, 23, 36, 1, 53, 36, 33
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


LINKS

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


FORMULA

a(n) = Sum_{dn, d<n} A033879(d).
a(n) = A296075(n)  A033879(n).


EXAMPLE

For n = 6, whose proper divisors are 1, 2, 3, their deficiencies are 1, 1, 2, thus a(6) = 1+1+2 = 4.
For n = 12, whose proper divisors are 1, 2, 3, 4, 6, their deficiencies are 1, 1, 2, 1, 0, thus a(12) = 1+1+2+1+0 = 5.


PROG

(PARI)
A033879(n) = ((2*n)sigma(n));
A296074(n) = sumdiv(n, d, (d<n)*A033879(d));


CROSSREFS

Cf. A033879.
Cf. also A294886, A294887, A294888, A294889, A293438 (product of).
Sequence in context: A243504 A292257 A317837 * A239451 A216223 A078072
Adjacent sequences: A296071 A296072 A296073 * A296075 A296076 A296077


KEYWORD

sign


AUTHOR

Antti Karttunen, Dec 04 2017


STATUS

approved



