A371885 a(n) is the least number k such that the sum of the final digits of the prime-power divisors of k (including 1) is n.

1, 11, 2, 3, 33, 5, 4, 7, 15, 12, 21, 20, 9, 28, 8, 76, 49, 24, 36, 27, 16, 54, 32, 48, 135, 80, 64, 112, 240, 192, 336, 320, 144, 216, 128, 1216, 784, 384, 576, 432, 256, 864, 512, 768, 2160, 1280, 1024, 1792, 3840, 3072, 5376, 5120, 2304, 3456, 2048, 19456, 12544, 6144, 9216, 6912, 4096, 13824

Offset: 1

Author

Robert Israel, Apr 10 2024

Keywords

• nonn
• base
• easy

Comments

a(n) is the least k such that A367502(k) = n.

Examples

			a(17) = 49 because the prime-power divisors of 49 are 1, 7 and 49, the sum of their final digits is 1 + 7 + 9 = 17, and 49 is the least number that works.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16).

Crossrefs

Cf. A000961, A367502.

Programs

Maple

f:= proc(n) local F,i,j,t;
  F:= ifactors(n)[2];
  1 + add(add(F[i,1]^j mod 10, j = 1 .. F[i,2]),i=1..nops(F))
end proc:
V:= Vector(100): count:= 0:
for n from 1 do
  v:= f(n);
  if v <= 100 and V[v] = 0 then V[v]:= n; count:= count+1;
      if count = 100 then break fi fi
od:
convert(V,list);

Formula

G.f.: (1 + 11*x + 2*x^2 + 3*x^3 + 33*x^4 + 5*x^5 + 4*x^6 + 7*x^7 + 15*x^8 + 12*x^9 + 21*x^10 + 20*x^11 + 9*x^12 + 28*x^13 + 8*x^14 + 76*x^15 + 49*x^16 + 24*x^17 + 36*x^18 + 27*x^19 - 122*x^21 - 393*x^24 - 232*x^33)/(1 - 16*x^20).

a(n + 20) = 16 * a(n) for n >= 15.