A371885 - OEIS

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

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..62.

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).

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.

EXAMPLE

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.

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);