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

Author

Jason G. Wurtzel, Nov 25 2006

Keywords

• easy
• nonn

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

Examples

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

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_)

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).

Programs

Magma

[n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -16]; // Vincenzo Librandi, Sep 14 2016

Mathematica

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

PARI

for(n=1,1000000,if(((sigma(n)-2*n)==-16),print1(n,",")))

Extensions

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