%I #33 Jan 26 2021 02:37:10

%S 965,8150,12966911,625261742

%N Nonpalindromic numbers n with property that the sum of the reversed divisors of n is equal to n+1.

%C Palindromes are excluded because palindromic primes automatically have this property, and palindromic nonprimes never have it.

%C Call a number "quasi-perfect" or "slightly excessive" if sigma(n) = 2n+1 (cf. A000203). It is conjectured that no quasi-perfect number exists. The present sequence is a variation that certainly has at least four terms.

%C a(5) > 10^11. - _Donovan Johnson_, May 26 2013

%C a(5) > 10^12. - _Giovanni Resta_, Aug 19 2019

%H Jason Earls, <a href="http://voices.yahoo.com/all-reversed-slightly-excessive-numbers-1315225.html">All About Reversed Slightly Excessive Numbers</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QuasiperfectNumber.html">Quasi-perfect number</a>

%e The divisors of 965 are 1, 5, 193, 965, and reversing and adding produces 1 + 5 + 391 + 569 = 966.

%o (Python)

%o from sympy import divisors

%o def ispal(n): s = str(n); return s == s[::-1]

%o def ok(n):

%o return not ispal(n) and n+1 == sum(int(str(d)[::-1]) for d in divisors(n))

%o print([m for m in range(10**4) if ok(m)]) # _Michael S. Branicky_, Jan 25 2021

%Y Cf. A069192, A069250, A000203.

%K nonn,base,more

%O 1,1

%A _N. J. A. Sloane_, May 19 2013

%E a(4) from _Donovan Johnson_, May 19 2013