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 A074730 Squares whose sum of anti-divisors is a square. 1
 1, 121, 169, 841, 2047288797225, 61838862885361 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 15 14:58 EDT 2024. Contains 371692 sequences. (Running on oeis4.)