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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
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
1,2
COMMENTS
a(n) is the least k such that A367502(k) = n.
LINKS
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);
CROSSREFS
Sequence in context: A088277 A089744 A160137 * A107698 A068164 A089754
KEYWORD
nonn,base,easy
AUTHOR
Robert Israel, Apr 10 2024
STATUS
approved