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A057530 n is odd and divisible by number of divisors of n and sum of digits of n.

%I A057530 #16 Oct 27 2023 22:00:46
%S A057530 1,9,225,441,1521,2025,2601,12321,40401,62001,99225,103041,251001,
%T A057530 321489,585225,893025,1022121,1108809,1212201,1320201,1946025,2368521,
%U A057530 2480625,2772225,3101121,3744225,4473225,4862025,5517801,6125625
%N A057530 n is odd and divisible by number of divisors of n and sum of digits of n.
%C A057530 For most values (except 9,2025 and 99225) number of divisors of n = sum of digits of n, see A057531.
%C A057530 The above comment is wrong: for 16 out of the first 34 terms of the sequence, the number of divisors of n does not equal the sum of the digits of n. - _Harvey P. Dale_, Dec 31 2015
%C A057530 Since A000005(n) is odd, n must be a square. - _Robert Israel_, Oct 31 2019
%H A057530 Robert Israel, <a href="/A057530/b057530.txt">Table of n, a(n) for n = 1..10000</a>
%p A057530 filter:= proc(m) local n;
%p A057530   n:= m^2;
%p A057530   n mod numtheory:-tau(n) = 0 and n mod convert(convert(n,base,10),`+`) = 0
%p A057530 end proc:
%p A057530 map(`^`, select(filter, [seq(i,i=1..10000,2)]),2); # _Robert Israel_, Oct 31 2019
%t A057530 Select[Range[1,5*10^6,2],Divisible[#,DivisorSigma[0,#]] && Divisible[ #,Total[ IntegerDigits[#]]]&] (* _Harvey P. Dale_, Dec 31 2015 *)
%o A057530 (Magma) [k:k in [1..6000001 by 2]| IsIntegral(k/NumberOfDivisors(k)) and IsIntegral(k/&+Intseq(k))]; // _Marius A. Burtea_, Oct 31 2019
%Y A057530 Cf. A000005, A005349, A033950, A057529.
%K A057530 nonn,easy,base
%O A057530 1,2
%A A057530 _Asher Auel_, Sep 03 2000
%E A057530 More terms from _Harvey P. Dale_, Dec 31 2015