A307227 Numbers k such that A060648(k) is divisible by k.

1, 2, 105, 210, 20349, 36075, 40698, 72150, 7162155, 9258795, 14324310, 18517590, 117972855, 156818025, 235945710, 313636050, 5448196215, 10896392430

Offset: 1

Author

Amiram Eldar, Mar 29 2019

Keywords

• nonn
• more

Comments

If k is an odd term of this sequence then 2*k is also a term.

The quotients A060648(a(n))/a(n) are 1, 2, 3, 6, 3, 3, 6, 6, 5, 5, 10, 10, 5, 5, 10, 10, ...

Also terms are: 75293843625, 89741043315, 150587687250, 179482086630, 459768040875, 919536081750, 1871844556725, 3743689113450, 30832458453225, 57275447662125, 61664916906450, 114550895324250. - David A. Corneth, Mar 29 2019

Crossrefs

Cf. A060648.

Programs

Mathematica

f[p_, e_] := (p^(e + 1) + p^e - 2)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; aQ[n_] := Divisible[a[n], n]; Select[Range[10^7], aQ]

PARI

f(n) = sumdiv(n, d,  2^omega(d)*(n/d) ); \\ A060648
isok(n) = !(f(n) % n); \\ Michel Marcus, Mar 30 2019

PARI

\\ for is(n), see isok(n) above \\ David A. Corneth, Mar 30 2019
A060648(n) = {my(f = factor(n), res = 1); for(i = 1, #f~, res *= (f[i, 1]^(f[i, 2]+1)+f[i, 1]^f[i, 2]-2)/(f[i, 1]-1)); res} \\ David A. Corneth, Mar 30 2019