OFFSET
1,2
COMMENTS
If p is prime, a(p) = Sum_{p|d} d * rad(d) = 1*1 + p*p = p^2 + 1.
FORMULA
a(prime(n)) = A066872(n). - Michel Marcus, Jun 12 2021
EXAMPLE
a(10) = Sum_{d|10} d * rad(d) = 1*1 + 2*2 + 5*5 + 10*10 = 1 + 4 + 25 + 100 = 130.
MATHEMATICA
Table[Sum[i (1 - Ceiling[n/i] + Floor[n/i]) Product[k^((PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[i/k] + Floor[i/k])), {k, i}], {i, n}], {n, 80}]
PROG
(PARI) rad(n) = factorback(factorint(n)[, 1]);
a(n) = sumdiv(n, d, d*rad(d)); \\ Michel Marcus, Jun 12 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 12 2021
STATUS
approved