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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 A037050 A275028

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 November 27 19:23 EST 2022. Contains 358406 sequences. (Running on oeis4.)