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%I #24 Feb 19 2022 04:52:04
%S 1,2,3,1,1,2,3,4,1,1,2,3,4,3,2,3,4,3,2,3,1,1,2,1,3,2,2,2,1,2,1,1,2,3,
%T 4,2,2,3,4,5,3,3,4,5,3,3,2,4,3,2,2,1,2,2,2,1,1,1,2,1,1,2,3,4,3,3,2,3,
%U 4,5,3,2,4,5,2,2,3,3,3,3,2,2,2,3,2,1,3,4,3,4,5
%N a(n) is the quotient obtained when digsum(m^2) is divided by digsum(m), with digsum = sum of digits = A007953 and m = A351650(n).
%C All positive integers are terms of this sequence (see A280012).
%C a(n) = 1 iff m = A351650(n) is a term of A058369 \ {0}.
%C a(n) = digsum(n) if m = A351650(n) is a term of A061909 \ {0}.
%H Diophante, <a href="http://www.diophante.fr/problemes-par-themes/arithmetique-et-algebre/a1-pot-pourri/4786-a1730-des-chiffres-a-sommer-pour-un-entier">A1730 - Des chiffres à sommer pour un entier</a> (in French).
%F a(n) = A004159(A351650(n)) / A007953(A351650(n)).
%e A351650(8) = 13, then digsum(13) = 1+3 = 4 while digsum(13^2) = digsum(169) = 1+6+9 = 16; hence, a(8) = 16/4 = 4.
%t Select[Total[IntegerDigits[#^2]]/Total[IntegerDigits[#]]& /@ Range[300], IntegerQ] (* _Amiram Eldar_, Feb 16 2022 *)
%o (PARI) lista(nn) = {my(list = List(), q); for (n=1, nn, if (denominator(q=sumdigits(n^2)/sumdigits(n))==1, listput(list, q));); Vec(list);} \\ _Michel Marcus_, Feb 16 2022
%Y Cf. A002283, A004159, A007953, A058369, A061909, A254066, A280012, A351650.
%K nonn,base
%O 1,2
%A _Bernard Schott_, Feb 16 2022
%E More terms from _Michel Marcus_, Feb 16 2022