A254618 a(n) = k-tuple deficiency of n-th deficient number.

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

Paolo P. Lava, Table of n, a(n) for n = 1..1000

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

Cf. A000027, A005100, A081705, A098007, A098008, A234899.

Sequence in context: A239585 A321788 A182093 * A268672 A054483 A258568

Adjacent sequences: A254615 A254616 A254617 * A254619 A254620 A254621

Keyword

nonn

Author

Paolo P. Lava, Feb 03 2015

Status

approved