login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 A341373 A287203

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 03:49 EST 2021. Contains 349530 sequences. (Running on oeis4.)