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A225684
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Nonpalindromic numbers n with property that the sum of the reversed divisors of n is equal to n+1.
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0
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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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
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EXAMPLE
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The divisors of 965 are 1, 5, 193, 965, and reversing and adding produces 1 + 5 + 391 + 569 = 966.
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PROG
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(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
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CROSSREFS
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Cf. A069192, A069250, A000203.
Sequence in context: A267996 A093232 A252259 * A186468 A014363 A260291
Adjacent sequences: A225681 A225682 A225683 * A225685 A225686 A225687
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KEYWORD
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nonn,base,more
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AUTHOR
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N. J. A. Sloane, May 19 2013
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EXTENSIONS
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a(4) from Donovan Johnson, May 19 2013
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STATUS
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approved
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