A125248 Numbers n whose abundance sigma(n)-2n = -16. Numbers n whose deficiency is 16.

17, 38, 92, 170, 248, 752, 988, 2528, 8648, 12008, 34688, 63248, 117808, 526688, 531968, 820808, 1292768, 1495688, 2095208, 2112512, 3477608, 4495808, 8419328, 12026888, 13192768, 16102808, 26347688, 29322008, 33653888, 169371008

Offset

1,1

Comments

When p=2^k+15 is prime (cf. A057197), then 2^(k-1)*p is in this sequence. The terms { 17, 38, 92, 248, 752, 2528, 34688, 531968, 2112512, 8419328, 537116672, 2147975168, ...} are of this from, with k in {1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, ...} = A057197. - M. F. Hasler, Jul 18 2016

Any term x of this sequence can be combined with any term y of A141547 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

Donovan Johnson, Giovanni Resta and Hiroaki Yamanouchi, Table of n, a(n) for n = 1..69 (terms <= 10^18, first 43 terms from Donovan Johnson and a(44)-a(51) from Giovanni Resta)

Example

The abundance of 38 = (1+2+19+38)-76 = -16

Mathematica

Select[Range[1, 10^6], DivisorSigma[1, #] - 2 # == - 16 &] (* Vincenzo Librandi, Sep 14 2016 *)

Prog

(PARI) for(n=1, 1000000, if(((sigma(n)-2*n)==-16), print1(n, ", ")))
(Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -16]; // Vincenzo Librandi, Sep 14 2016

Crossrefs

Cf. A000203, A033880, A005100; A191363 (deficiency 2), A125246 (deficiency 4), A141548 (deficiency 6), A125247 (deficiency 8), A101223 (deficiency 10), A141549 (deficiency 12), A141550 (deficiency 14), A125248 (this), A223608 (deficiency 18), A223607 (deficiency 20); A141547 (abundance 16).

Sequence in context: A051779 A139579 A293206 * A259489 A226127 A156777

Adjacent sequences: A125245 A125246 A125247 * A125249 A125250 A125251

Keyword

easy,nonn

Author

Jason G. Wurtzel, Nov 25 2006

Extensions

a(17) to a(30) from Klaus Brockhaus, Nov 29 2006

Status

approved