A101223 Numbers m whose deficiency is 10, or: sigma(m) = 2m - 10.

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

Offset: 1

Author

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

Keywords

• nonn
• more

Comments

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^(k-1)*(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

Examples

			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.
		

Crossrefs

Cf. A033879, A033880, A125246 (deficiency 4), A141548 (deficiency 6), A125247 (deficiency 8), A125248 (deficiency 16).

Cf. also A274556.

Cf. A223609 (abundance 10).

Programs

Magma

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

Mathematica

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

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