

A217769


Least number k > n such that sigma(k) = 2*(kn), or 0 if no such k exists.


2



6, 3, 5, 7, 22, 11, 13, 27, 17, 19, 46, 23, 124, 58, 29, 31, 250, 57, 37, 55, 41, 43, 94, 47, 1264, 106, 53, 87, 118, 59, 61, 85, 134, 67, 142, 71, 73, 712, 158, 79, 166, 83, 405, 115, 89, 141, 406, 119, 97, 202, 101, 103, 214, 107, 109, 145, 113, 177, 418, 143
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OFFSET

0,1


COMMENTS

a(0) = 6 corresponds to the smallest perfect number.
Is n = 144 the first number for which a(n) = 0?  T. D. Noe, Mar 28 2013
No, a(144) = 95501968.  Giovanni Resta, Mar 28 2013
We can instead compute k  sigma(k)/2 for increasing k, which is computationally much faster. In this case, we stop computing when all n have been found for a range of numbers.  T. D. Noe, Mar 28 2013
Also, the first number whose deficiency is 2n. This is the even bisection of A082730. Hence, the first number in the following sequences: A000396, A191363, A125246, A141548, A125247, A101223, A141549, A141550, A125248, A223608, A223607, A223606.  T. D. Noe, Mar 29 2013
10^12 < a(654) <= 618970019665683124609613824.  Donovan Johnson, Jan 04 2014


LINKS

T. D. Noe and Donovan Johnson, Table of n, a(n) for n = 0..653 (first 241 terms from T. D. Noe)
Nichole Davis, Dominic Klyve and Nicole Kraght, On the difference between an integer and the sum of its proper divisors, Involve, Vol. 6 (2013), No. 4, 493504; DOI: 10.2140/involve.2013.6.493.


EXAMPLE

a(4)=22, since 22 is the least number such that sigma(22)=36=2*(224).


MATHEMATICA

Table[Min[Select[Range[2000], DivisorSigma[1, #] == 2*(#  i) &]], {i, 0, 60}]
nn = 144; t = Table[0, {nn}]; k = 0; While[k++; Times @@ t == 0, s = (2*k  DivisorSigma[1, k])/2; If[s >= 0 && s < nn && IntegerQ[s] && t[[s + 1]] == 0, t[[s + 1]] = k]]; t (* T. D. Noe, Mar 28 2013 *)


CROSSREFS

Cf. A000203, A000396.
Cf. A087998 (negative n).
Sequence in context: A199867 A171030 A294386 * A296501 A296491 A085653
Adjacent sequences: A217766 A217767 A217768 * A217770 A217771 A217772


KEYWORD

nonn


AUTHOR

Jayanta Basu, Mar 28 2013


STATUS

approved



