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

1,2

Comments

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

Links

Table of n, a(n) for n=1..54.

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

Cf. A007947 (rad), A066872.

Sequence in context: A272267 A195735 A061145 * A321558 A328667 A317966

Adjacent sequences: A345258 A345259 A345260 * A345262 A345263 A345264

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2021

Status

approved