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A125248
Numbers n whose abundance sigma(n)-2n = -16. Numbers n whose deficiency is 16.
12
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
KEYWORD
easy,nonn
AUTHOR
Jason G. Wurtzel, Nov 25 2006
EXTENSIONS
a(17) to a(30) from Klaus Brockhaus, Nov 29 2006
STATUS
approved