OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 1 + Sum_{d|n, d>1} floor(1/omega(d)) * (d mod 10).
EXAMPLE
a(16) = 21 since the prime power divisors of 16 are {1, 2, 4, 8, 16} and the sum of their final digits is 1 + 2 + 4 + 8 + 6 = 21.
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:
map(f, [$1..100]); # Robert Israel, Apr 10 2024
MATHEMATICA
Table[1 + Sum[Floor[1/PrimeNu[k]] Mod[k, 10] (1 - Ceiling[n/k] + Floor[n/k]), {k, 2, n}], {n, 100}]
PROG
(PARI) a(n) = my(f=factor(n)); 1 + sum(k=1, #f~, sum(j=1, f[k, 2], lift(Mod(f[k, 1], 10)^j))); \\ Michel Marcus, Nov 22 2023
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Wesley Ivan Hurt, Nov 20 2023
STATUS
approved