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A076624 Sum of the non-divisors of n between 1 and n is a perfect square. 0

%I #10 Jun 24 2014 01:08:32

%S 1,2,5,6,14,149,158,384,846,5065,8648,181166,196366,947545,5821349,

%T 55867168,491372910,4273496001,40534401950,87226316289

%N Sum of the non-divisors of n between 1 and n is a perfect square.

%C Define b(0)=2, b(1)=5 and b(n)=6*b(n-1)-b(n-2)-2 for n>1. A prime number p is in the sequence iff (p^2-p-2)/2 is a square iff p=b(n) for some n. The next prime in the sequence is b(21)=8946229758127349, followed by b(n) for n=33, 51, 57 and 75.

%C a(21) > 2*10^11. - Donovan Johnson, Jul 09 2011

%F s(n)=A000217[n]-A000203[n]=A024816[n] is a square.

%e The sum of the non-divisors of 14 between 1 and 14 is 3 + 4 + 5 + 6 + 8 + 9 + 10 + 11 + 12 + 13 = 81 = 9^2. 1, 2, 7 & 14 are divisors. Hence 14 is a term of the sequence.

%t Select[ Range[14*10^6], IntegerQ[Sqrt[(# (# + 1)/2) - DivisorSigma[1, # ]]] &]

%K nonn

%O 1,2

%A _Joseph L. Pe_, Oct 22 2002

%E Edited by _Robert G. Wilson v_ and _Dean Hickerson_, Oct 25 2002

%E a(16)-a(17) from _Donovan Johnson_, Oct 14 2009

%E a(18)-a(20) from _Donovan Johnson_, Jul 09 2011

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Last modified March 29 09:32 EDT 2024. Contains 371268 sequences. (Running on oeis4.)