A345261 a(n) = Sum_{d|n} d * rad(d).
1, 5, 10, 13, 26, 50, 50, 29, 37, 130, 122, 130, 170, 250, 260, 61, 290, 185, 362, 338, 500, 610, 530, 290, 151, 850, 118, 650, 842, 1300, 962, 125, 1220, 1450, 1300, 481, 1370, 1810, 1700, 754, 1682, 2500, 1850, 1586, 962, 2650, 2210, 610, 393, 755, 2900, 2210, 2810, 590
Offset: 1
Keywords
Examples
a(10) = Sum_{d|10} d * rad(d) = 1*1 + 2*2 + 5*5 + 10*10 = 1 + 4 + 25 + 100 = 130.
Programs
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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}] -
PARI
rad(n) = factorback(factorint(n)[, 1]); a(n) = sumdiv(n, d, d*rad(d)); \\ Michel Marcus, Jun 12 2021
Formula
a(prime(n)) = A066872(n). - Michel Marcus, Jun 12 2021
Comments