cp's OEIS Frontend

A366512 Numbers k such that the square of the sum of the digits times the sum of the cubes of the digits equals k.

%I A366512 #29 Mar 25 2024 12:05:28
%S A366512 1,32144,37000,111616,382360
%N A366512 Numbers k such that the square of the sum of the digits times the sum of the cubes of the digits equals k.
%C A366512 There are exactly 5 such numbers (Property 14 of Clerc).
%H A366512 René-Louis Clerc, <a href="https://hal.science/hal-04235744">Quelques nombres de Niven-Harshad particuliers</a>, pp. 1-17, hal-04235744, 2023.
%H A366512 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 A366512 32144 = ((3+2+1+4+4)^2)*(3^3 + 2^3 + 1^3 + 4^3 + 4^3) = 196*164.
%t A366512 Select[Range[10^6], #1 == Total[#2]^2*Total[#2^3] & @@ {#, IntegerDigits[#]} &] (* _Michael De Vlieger_, Mar 25 2024 *)
%o A366512 (PARI) niven23()={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,if((a+b+c+d+e+f+g+h)^2*(a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3)==10000000*a+1000000*b+100000*c+10000*d+1000*e+100*f+10*g+h,print1(10000000*a+1000000*b+100000*c+10000*d+1000*e+100*f+10*g+h,", "))))))))))}
%o A366512 (PARI) isok(k) = my(d=digits(k)); vecsum(d)^2*sum(i=1, #d, d[i]^3) == k; \\ _Michel Marcus_, Oct 12 2023
%Y A366512 Cf. A115518, A257766, A061209, A061210, A254000, A130680.
%K A366512 nonn,base,fini,full
%O A366512 1,2
%A A366512 _René-Louis Clerc_, Oct 11 2023