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A254618
a(n) = k-tuple deficiency of n-th deficient number.
1
1, 2, 2, 3, 2, 2, 3, 4, 4, 2, 2, 5, 5, 6, 2, 2, 3, 6, 2, 1, 7, 3, 2, 2, 3, 6, 1, 3, 2, 7, 3, 2, 2, 1, 7, 8, 2, 4, 3, 4, 9, 2, 3, 3, 4, 2, 2, 2, 3, 4, 3, 2, 5, 4, 2, 2, 1, 5, 5, 3, 2, 1, 2, 2, 3, 9, 7, 2, 4, 6, 4, 4, 2, 2, 3, 4, 2, 2, 8, 1, 2, 2, 2, 3, 2, 3, 5
OFFSET
1,2
COMMENTS
For any deficient number x iterate the process f(x)=sigma(x)-x. Sequence lists how many times f(x) keeps deficient until it reaches zero.
Non-deficient numbers are excluded from this sequence.
k-tuple deficiency records is A000027.
k-tuple deficiency record-holders is A234899.
LINKS
EXAMPLE
a(20) = 1 because the 20th deficient number is 25 and:
1) f(25) = sigma(25) - 25 = 6 < 25.
We must stop here because 6 is abundant.
a(21) = 7 because the 21st deficient number is 26 and:
1) f(26) = sigma(26) - 26 = 16 < 26;
2) f(16) = sigma(16) - 16 = 15 < 16;
3) f(15) = sigma(15) - 15 = 9 < 15;
4) f(9) = sigma(9) - 9 = 4 < 9;
5) f(4) = sigma(4) - 4 = 3 < 4;
6) f(3) = sigma(3) - 3 = 2 < 1;
7) f(1) = sigma(1) - 1 = 0 < 1.
We must stop here because sigma(0) is not defined.
MAPLE
with(numtheory): P:=proc(q) local a, b, n, t;
for n from 1 to q do t:=0; b:=sigma(n)-n; a:=n;
if b<a then while b<a do t:=t+1; a:=b; b:=sigma(b)-b; od;
print(t); fi; od; end: P(10^3);
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Feb 03 2015
STATUS
approved