

A101223


Numbers n whose deficiency is 10, or: sigma(n) = 2n  10.


10



11, 21, 26, 68, 656, 2336, 8768, 133376, 528896, 34360918016, 35184409837568, 576460757135261696
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OFFSET

1,1


COMMENTS

Or, numbers n which satisfy 2n+1sigma(n) = 11.
Call a number that satisfies the equation 2n+1sigma(n) = x "cofacient" (from Latin "co" and "facient"  "look") numbers of type x. It's easy to see that the perfect numbers are cofacient of type 1, the numbers 2^N are cofacient of type 2 (it is an open question whether there can be cofacient numbers of type 2 that are not powers of 2) and all prime numbers p are cofacient of type p.
No other terms below 5.6*10^8.  Robert G. Wilson v, Dec 15 2004
a(11) > 10^12.  Donovan Johnson, Dec 08 2011
a(11) > 10^13.  Giovanni Resta, Mar 29 2013
a(13) > 10^18.  Hiroaki Yamanouchi, Aug 21 2018
A subsequence of A274556. a(11) <= b(23) = 35184409837568 ~ 3.5*10^13, since b(k) := 2^(k1)*(2^k+9) is in this sequence for all k in A057196 (2^k+9 is prime). All known terms except a(2) = 21 are of that form.  M. F. Hasler, Jul 18 2016
Any term x of this sequence can be combined with any term y of A223609 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable.  Timothy L. Tiffin, Sep 13 2016


LINKS

Table of n, a(n) for n=1..12.
V. K. Tintschev, Cofacient numbers.


EXAMPLE

The divisors of 68 are {1, 2, 4, 17, 34, 68} and so sigma(68) = 1 + 2 + 4 + 17+ 24 + 68 = 126 = 2*68  10; thus, the deficiency of 68 is 10 so 68 is a term of the sequence.


MATHEMATICA

Select[ Range[ 85000000], DivisorSigma[1, # ] + 10 == 2# &]


PROG

(MAGMA) [n: n in [1..9*10^6]  (SumOfDivisors(n)) eq 2*n10]; // Vincenzo Librandi, Sep 15 2016


CROSSREFS

Cf. A033880, A125246 (deficiency 4), A141548 (deficiency 6), A125247 (deficiency 8), A125248 (deficiency 16).
Cf. also A274556.
Cf. A223609 (abundance 10)
Sequence in context: A261409 A195100 A125164 * A109686 A077522 A049201
Adjacent sequences: A101220 A101221 A101222 * A101224 A101225 A101226


KEYWORD

nonn,more


AUTHOR

Vassil K. Tintschev (tinchev(AT)sunhe.jinr.ru), Dec 15 2004


EXTENSIONS

Edited and extended by Robert G. Wilson v, Dec 15 2004
a(10) from Donovan Johnson, Dec 23 2008
Edited by M. F. Hasler, Jul 18 2016
a(11)a(12) from Hiroaki Yamanouchi, Aug 21 2018


STATUS

approved



