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

Author

N. J. A. Sloane, May 19 2013

Keywords

• nonn
• base
• more

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

Examples

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

Links

• Jason Earls, All About Reversed Slightly Excessive Numbers
• Eric Weisstein's World of Mathematics, Quasi-perfect number

Crossrefs

Cf. A069192, A069250, A000203.

Programs

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

Extensions

a(4) from Donovan Johnson, May 19 2013