A398342 - OEIS

A398342

Numbers k, such that Sum_{d|k} rad(d) is a multiple of rad(k), where rad = A007947.

1, 6, 20, 48, 54, 56, 60, 126, 135, 180, 270, 352, 384, 432, 441, 486, 500, 540, 640, 832, 1008, 1056, 1080, 1100, 1176, 1260, 1350, 1620, 1920, 1960, 2106, 2160, 2205, 2744, 3072, 3168, 3300, 3456, 3888, 4320, 4352, 4374, 4410, 4860, 5760, 5824, 5880, 6174

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OFFSET

1,2

LINKS

Žiga Pirc, Table of n, a(n) for n = 1..1200

EXAMPLE

a(2) = 6 = 2*3; 6 is squarefree, thus rad(6) = 6, with divisors {1, 2, 3, 6}, all squarefree. The sum of divisors is 12, a multiple of 6. - Michael De Vlieger, Sep 01 2026

Prime factorization of 20 is 2^2*5, so rad(20) = 10. rad(1) + rad(2) + rad(4) + rad(5) + rad(10) + rad(20) = 30, so 3*10.

MATHEMATICA

f[p_, e_] := (1 + e*p)/p; q[1] = True; q[k_] := IntegerQ[Times @@ f @@@ FactorInteger[k]]; Select[Range[6500], q] (* Amiram Eldar, Sep 01 2026 *)

PROG

(PARI) is_ok(n) = sumdiv(n, d, factorback(factorint(d)[, 1])) % factorback(factorint(n)[, 1]) == 0

CROSSREFS

Cf. A007947, A191750.

Sequence in context: A005564 A011928 A394826 * A055455 A203552 A331754

Adjacent sequences: A398336 A398338 A398339 * A398348 A398349 A398350

KEYWORD

nonn,new

AUTHOR

Žiga Pirc, Sep 01 2026

STATUS

approved