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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.

%I A203616 #21 Feb 12 2024 09:19:42
%S A203616 1,2,3,4,5,6,8,9,20,63,96,97,317,596,1473,3934,26777,27684,50867,
%T A203616 51767,62417,322001,393216,1308775,1420260,1851474,2651867,2659067,
%U A203616 3040656,3227267,3289277,3376007,4626917,4639067,5378507,6054521,6227027,6239839,6439067,6581929
%N 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.
%C A203616 A066466 is a subsequence of this sequence.
%H A203616 Dumitru Damian, <a href="/A203616/b203616.txt">Table of n, a(n) for n = 1..235</a> (terms up to 10^9)
%e A203616 n=317. Anti-divisors: 2, 3, 5, 127, 211.
%e A203616 Sum of the reversals of the anti-divisors: 2+3+5+721+112=843.
%e A203616 Sigma*(317)=348 and its reversal is 843.
%e A203616 n=1473. Anti-divisors: 2, 5, 6, 7, 19, 31, 95, 155, 421, 589, 982.
%e A203616 Sum of the reversals of the anti-divisors:
%e A203616 2+5+6+7+91+13+59+551+124+985+289=2132.
%e A203616 Sigma*(1473)=2312 and its reversal is 2132.
%p A203616 isA203616:=proc(j) local a,b,c;   a:=0; b:=0;
%p A203616    for c from 2 to j-1 do
%p A203616      if abs((j mod c)-c/2)<1 then a:=a+A004086(c); b:=b+c; fi;
%p A203616    od;
%p A203616 evalb(A004086(b)=a) end: # simplified by _M. F. Hasler_, Jan 29 2012
%p A203616 for n to 10^7 do if isA203616(n) then lprint(n) fi od: # simplified by _M. F. Hasler_, Jan 29 2012
%o A203616 (Python)
%o A203616 from itertools import count, islice
%o A203616 from sympy.ntheory.factor_ import antidivisors
%o A203616 def a203616():
%o A203616     isa = lambda n: str(sum((a:=antidivisors(n))))[::-1]==str(sum(map(int, (str(_)[::-1] for _ in a))))
%o A203616     yield from (n for n in count(1) if isa(n))
%o A203616 a203616_list = [*islice(a203616(), 20)] # _Dumitru Damian_, Feb 12 2024
%Y A203616 Cf. A004086, A066272, A066466, A069942, A195144, A203615.
%K A203616 nonn,base
%O A203616 1,2
%A A203616 _Paolo P. Lava_, Jan 20 2012
%E A203616 a(22)-a(40) from _Dumitru Damian_, Feb 12 2024