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

1, 32144, 37000, 111616, 382360

Offset

1,2

Comments

There are exactly 5 such numbers (Property 14 of Clerc).

Links

Table of n, a(n) for n=1..5.

René-Louis Clerc, Quelques nombres de Niven-Harshad particuliers, pp. 1-17, hal-04235744, 2023.

René-Louis Clerc, Nombres S+P, maxSP, minSP et |P-S|, hal-04507547 [math.nt], 2024. (In French)

Example

32144 = ((3+2+1+4+4)^2)*(3^3 + 2^3 + 1^3 + 4^3 + 4^3) = 196*164.

Mathematica

Select[Range[10^6], #1 == Total[#2]^2*Total[#2^3] & @@ {#, IntegerDigits[#]} &] (* Michael De Vlieger, Mar 25 2024 *)

Prog

(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, ", "))))))))))}
(PARI) isok(k) = my(d=digits(k)); vecsum(d)^2*sum(i=1, #d, d[i]^3) == k; \\ Michel Marcus, Oct 12 2023

Crossrefs

Cf. A115518, A257766, A061209, A061210, A254000, A130680.

Sequence in context: A264499 A249230 A250897 * A146896 A205930 A269930

Adjacent sequences: A366509 A366510 A366511 * A366513 A366514 A366515

Keyword

nonn,base,fini,full

Author

René-Louis Clerc, Oct 11 2023

Status

approved