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A358512 a(n) is the smallest number k with exactly n divisors that can be written in the form m + digsum(m), for some m (A176995).

%I A358512 #20 Mar 02 2023 11:25:00
%S A358512 1,2,4,8,12,30,24,80,48,72,96,192,120,180,288,612,240,624,420,360,480,
%T A358512 900,1632,960,1200,720,840,1560,2100,1260,1440,3420,2640,3024,1680,
%U A358512 2880,8316,4620,3600,3780,4200,2520,3360,6240,9900,6300,7200,8640,6720,13200,7920
%N A358512 a(n) is the smallest number k with exactly n divisors that can be written in the form m + digsum(m), for some m (A176995).
%H A358512 David A. Corneth, <a href="/A358512/b358512.txt">Table of n, a(n) for n = 0..2499</a>
%e A358512 1 cannot be written in the form m + digsum(m), so a(0) = 1.
%e A358512 2 has divisors 1 and 2, and only 2 is written 2 = 1 + digsum(1), so a(1) = 2.
%e A358512 3 has divisors 1 and 3 that cannot be written in the form m + digsum(m).
%e A358512 4 has divisors 1, 2, 4, but only 2 = 1 + digsum(1) and 4 = 2 + digsum(2), so a(2) = 4.
%o A358512 (Magma) f:=func<n|exists(c){s:s in [0..n]| n eq s+&+Intseq(s)}>; a:=[]; for n in [0..50] do k:=1; while #[d:d in Divisors(k)|f(d)] ne n do k:=k+1; end while; Append(~a,k); end for; a;
%o A358512 (PARI) is_A003052(n)={for(i=1, min(n\2, 9*#digits(n)), sumdigits(n-i)==i && return); n}
%o A358512 a(n) = my(k=1); while (sumdiv(k, d, !is_A003052(d)) != n, k++); k; \\ _Michel Marcus_, Dec 13 2022
%Y A358512 Cf. A003052, A062028, A176995, A230093.
%K A358512 nonn,base
%O A358512 0,2
%A A358512 _Marius A. Burtea_, Dec 04 2022