A367502 Sum of the final digits of the prime power divisors (p^k, k>=0) of n.

1, 3, 4, 7, 6, 6, 8, 15, 13, 8, 2, 10, 4, 10, 9, 21, 8, 15, 10, 12, 11, 4, 4, 18, 11, 6, 20, 14, 10, 11, 2, 23, 5, 10, 13, 19, 8, 12, 7, 20, 2, 13, 4, 8, 18, 6, 8, 24, 17, 13, 11, 10, 4, 22, 7, 22, 13, 12, 10, 15, 2, 4, 20, 27, 9, 7, 8, 14, 7, 15, 2, 27, 4, 10, 14, 16, 9, 9, 10, 26, 21, 4, 4

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

Cf. A000961 (Powers of primes), A001221 (omega), A010879 (Final digit of n), A023888 (Sum of the prime power divisors of n including 1), A371885 (first k with a(k) = n).

Sequence in context: A322656 A105827 A230289 * A023888 A222085 A187793

Adjacent sequences: A367499 A367500 A367501 * A367503 A367504 A367505

Keyword

nonn,easy,base

Author

Wesley Ivan Hurt, Nov 20 2023

Status

approved