

A225684


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


0




OFFSET

1,1


COMMENTS

Palindromes are excluded because palindromic primes automatically have this property, and palindromic nonprimes never have it.
Call a number "quasiperfect" or "slightly excessive" if sigma(n) = 2n+1 (cf. A000203). It is conjectured that no quasiperfect number exists. The present sequence is a variation that certainly has at least four terms.
a(5) > 10^11.  Donovan Johnson, May 26 2013
a(5) > 10^12.  Giovanni Resta, Aug 19 2019


LINKS

Table of n, a(n) for n=1..4.
Jason Earls, All About Reversed Slightly Excessive Numbers
Eric Weisstein's World of Mathematics, Quasiperfect number


EXAMPLE

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


PROG

(Python)
from sympy import divisors
def ispal(n): s = str(n); return s == s[::1]
def ok(n):
return not ispal(n) and n+1 == sum(int(str(d)[::1]) for d in divisors(n))
print([m for m in range(10**4) if ok(m)]) # Michael S. Branicky, Jan 25 2021


CROSSREFS

Cf. A069192, A069250, A000203.
Sequence in context: A267996 A093232 A252259 * A186468 A014363 A260291
Adjacent sequences: A225681 A225682 A225683 * A225685 A225686 A225687


KEYWORD

nonn,base,more


AUTHOR

N. J. A. Sloane, May 19 2013


EXTENSIONS

a(4) from Donovan Johnson, May 19 2013


STATUS

approved



