A074730 Squares whose sum of anti-divisors is a square.

1, 121, 169, 841, 2047288797225, 61838862885361

Offset

1,2

Comments

See A066272 for definition of anti-divisor.

a(5), if it exists, is greater than 10^12. - Franklin T. Adams-Watters, Feb 08 2012

a(7) > 10^16. - Hiroaki Yamanouchi, Sep 27 2015

Links

Table of n, a(n) for n=1..6.

Prog

(Python)
from gmpy2 import is_square
from sympy import divisors
A074730 = [n for n in (x**2 for x in range(1, 10**4)) if is_square(int(sum([2*d for d in divisors(n) if n > 2*d and n%(2*d)] + [d for d in divisors(2*n-1) if n > d >=2 and n%d] + [d for d in divisors(2*n+1) if n > d >=2 and n%d])))]
# Chai Wah Wu, Aug 12 2014
(PARI) has(n)=my(k=valuation(n, 2)); issquare(sigma(2*n+1)+sigma(2*n-1)+sigma(n>>k)<<(k+1)-6*n-2)
print1(1); for(n=2, 1e6, if(has(n^2), print1(", "n^2))) \\ Charles R Greathouse IV, Nov 20 2015

Crossrefs

Cf. A066417.

Sequence in context: A240775 A346316 A284643 * A268519 A364778 A037050

Adjacent sequences: A074727 A074728 A074729 * A074731 A074732 A074733

Keyword

nonn

Author

Jason Earls, Sep 05 2002

Extensions

a(5)-a(6) from Hiroaki Yamanouchi, Sep 27 2015

Status

approved