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A307227 Numbers k such that A060648(k) is divisible by k. 0
1, 2, 105, 210, 20349, 36075, 40698, 72150, 7162155, 9258795, 14324310, 18517590, 117972855, 156818025, 235945710, 313636050, 5448196215, 10896392430 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..18.

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]

PROG

(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

CROSSREFS

Cf. A060648.

Sequence in context: A001184 A098653 A119433 * A042351 A258828 A156880

Adjacent sequences:  A307224 A307225 A307226 * A307228 A307229 A307230

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Mar 29 2019

STATUS

approved

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Last modified May 15 20:08 EDT 2021. Contains 343920 sequences. (Running on oeis4.)