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

11, 21, 26, 68, 656, 2336, 8768, 133376, 528896, 34360918016, 35184409837568, 576460757135261696, 9444732966357765718016, 9903520314283675517890592768

Offset

1,1

Comments

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

a(15) <= 2^56 * 144115188075855881. - Max Alekseyev, Feb 05 2026

Links

Table of n, a(n) for n=1..14.

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*n-10]; // Vincenzo Librandi, Sep 15 2016

Crossrefs

Subsequence of A274556.

Deficiency k: A191363 (k=2), A125246 (k=4), A141548 (k=6), A125247 (k=8), A101223 (k=10), A141549 (k=12), A141550 (k=14), A125248 (k=16), A223608 (k=18), A223607 (k=20), A223606 (k=22), A385255 (k=24), A275702 (k=26), A387352 (k=32), A175730 (k=42), A101259 (k=54), A275997 (k=64).

Abundance k: A088831 (k=2), A088832 (k=4), A087167 (k=6), A088833 (k=8), A223609 (k=10), A141545 (k=12), A141546 (k=14), A141547 (k=16), A223610 (k=18), A223611 (k=20), A223612 (k=22), A223613 (k=24), A275701 (k=26), A175989 (k=32), A275996 (k=64), A292626 (k=128).

Cf. A033879, A033880, A057196.

Sequence in context: A261409 A195100 A125164 * A396129 A109686 A077522

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

Edited and a(13)-a(14) added by Max Alekseyev, Feb 05 2026

Status

approved