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A076624 Sum of the non-divisors of n between 1 and n is a perfect square. 0
1, 2, 5, 6, 14, 149, 158, 384, 846, 5065, 8648, 181166, 196366, 947545, 5821349, 55867168, 491372910, 4273496001, 40534401950, 87226316289 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

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

LINKS

Table of n, a(n) for n=1..20.

FORMULA

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

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

Sequence in context: A237352 A109784 A221472 * A205385 A287203 A193402

Adjacent sequences:  A076621 A076622 A076623 * A076625 A076626 A076627

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Oct 22 2002

EXTENSIONS

Edited by Robert G. Wilson v and Dean Hickerson, Oct 25 2002

a(16)-a(17) from Donovan Johnson, Oct 14 2009

a(18)-a(20) from Donovan Johnson, Jul 09 2011

STATUS

approved

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Last modified July 25 04:48 EDT 2017. Contains 289779 sequences.