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A203616
Numbers k such that the reversal of sigma*(k) equals the sum of the reversals of the anti-divisors of k, where sigma*(k) is the sum of the anti-divisors of k.
2
1, 2, 3, 4, 5, 6, 8, 9, 20, 63, 96, 97, 317, 596, 1473, 3934, 26777, 27684, 50867, 51767, 62417, 322001, 393216, 1308775, 1420260, 1851474, 2651867, 2659067, 3040656, 3227267, 3289277, 3376007, 4626917, 4639067, 5378507, 6054521, 6227027, 6239839, 6439067, 6581929
OFFSET
1,2
COMMENTS
A066466 is a subsequence of this sequence.
LINKS
Dumitru Damian, Table of n, a(n) for n = 1..235 (terms up to 10^9)
EXAMPLE
n=317. Anti-divisors: 2, 3, 5, 127, 211.
Sum of the reversals of the anti-divisors: 2+3+5+721+112=843.
Sigma*(317)=348 and its reversal is 843.
n=1473. Anti-divisors: 2, 5, 6, 7, 19, 31, 95, 155, 421, 589, 982.
Sum of the reversals of the anti-divisors:
2+5+6+7+91+13+59+551+124+985+289=2132.
Sigma*(1473)=2312 and its reversal is 2132.
MAPLE
isA203616:=proc(j) local a, b, c; a:=0; b:=0;
for c from 2 to j-1 do
if abs((j mod c)-c/2)<1 then a:=a+A004086(c); b:=b+c; fi;
od;
evalb(A004086(b)=a) end: # simplified by M. F. Hasler, Jan 29 2012
for n to 10^7 do if isA203616(n) then lprint(n) fi od: # simplified by M. F. Hasler, Jan 29 2012
PROG
(Python)
from itertools import count, islice
from sympy.ntheory.factor_ import antidivisors
def a203616():
isa = lambda n: str(sum((a:=antidivisors(n))))[::-1]==str(sum(map(int, (str(_)[::-1] for _ in a))))
yield from (n for n in count(1) if isa(n))
a203616_list = [*islice(a203616(), 20)] # Dumitru Damian, Feb 12 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Jan 20 2012
EXTENSIONS
a(22)-a(40) from Dumitru Damian, Feb 12 2024
STATUS
approved