A345261 - OEIS

%I #6 Jun 12 2021 18:38:28

%S 1,5,10,13,26,50,50,29,37,130,122,130,170,250,260,61,290,185,362,338,

%T 500,610,530,290,151,850,118,650,842,1300,962,125,1220,1450,1300,481,

%U 1370,1810,1700,754,1682,2500,1850,1586,962,2650,2210,610,393,755,2900,2210,2810,590

%N a(n) = Sum_{d|n} d * rad(d).

%C If p is prime, a(p) = Sum_{p|d} d * rad(d) = 1*1 + p*p = p^2 + 1.

%F a(prime(n)) = A066872(n). - _Michel Marcus_, Jun 12 2021

%e a(10) = Sum_{d|10} d * rad(d) = 1*1 + 2*2 + 5*5 + 10*10 = 1 + 4 + 25 + 100 = 130.

%t 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}]

%o (PARI) rad(n) = factorback(factorint(n)[, 1]);

%o a(n) = sumdiv(n, d, d*rad(d)); \\ _Michel Marcus_, Jun 12 2021

%Y Cf. A007947 (rad), A066872.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 12 2021