%I #30 Mar 25 2024 12:05:25
%S 1,4147200,12743163,21147075,39143552,52921472,156754936,205889445,
%T 233935967
%N Numbers k such that the sum of the digits of k times the square of the sum of the digits cubed of k equals k.
%C There are exactly 9 such numbers (Property 13 of Clerc).
%H René-Louis Clerc, <a href="https://hal.science/hal-04235744">Quelques nombres de Niven-Harshad particuliers</a>, pp. 1-17, hal-04235744, 2023.
%H René-Louis Clerc, <a href="https://ut3-toulouseinp.hal.science/hal-04507547">Nombres S+P, maxSP, minSP et |P-S|</a>, hal-04507547 [math.nt], 2024. (In French)
%e 4147200 = (4+1+4+7+2)*(4^3+1+4^3+7^3+2^3)^2 = 18*230400.
%o (PARI) niven12()={for(a=0,9,for(b=0,9,for(c=0,9,for(d=0,9,for(e=0,9,for(f=0,9,for(g=0,9,for(h=0,9,for(i=0,9,for(j=0,9,if((a+b+c+d+e+f+g+h+i+j)*(a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3+i^3+j^3)^2==1000000000*a+100000000*b+10000000*c+1000000*d+100000*e+10000*f+1000*g+100*h+10*i+j,print1(1000000000*a+100000000*b+10000000*c+1000000*d+100000*e+10000*f+1000*g+100*h+10*i+j,";"))))))))))))}
%o (PARI) isok(k) = my(d=digits(k)); vecsum(d)*sum(i=1, #d, d[i]^3)^2 == k; \\ _Michel Marcus_, Oct 12 2023
%Y Cf. A115518, A257766, A061209, A061210, A254000, A130680.
%K nonn,base,fini,full
%O 1,2
%A _René-Louis Clerc_, Oct 11 2023