A076624 Numbers k such that the sum of the non-divisors of k between 1 and k is a perfect square.

1, 2, 5, 6, 14, 149, 158, 384, 846, 5065, 8648, 181166, 196366, 947545, 5821349, 55867168, 491372910, 4273496001, 40534401950, 87226316289

Offset

1,2

Comments

Numbers k such that A024816(k) is a square.

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.

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

Cf. A024816.

Sequence in context: A237352 A109784 A221472 * A205385 A341373 A363132

Adjacent sequences: A076621 A076622 A076623 * A076625 A076626 A076627

Keyword

nonn,more

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

Edited by Michel Marcus, May 21 2025

Status

approved