A225684 Nonpalindromic numbers n with property that the sum of the reversed divisors of n is equal to n+1.

965, 8150, 12966911, 625261742

Offset

1,1

Comments

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

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.

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, Quasi-perfect 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 A345549 A345802

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