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A229323 Composite squarefree numbers n such that p - tau(n) divides n - phi(n), where p are the prime factors of n, tau(n) = A000005(n) and phi(n) = A000010(n). 2
6, 10, 15, 21, 42, 28101, 38505, 5298186, 8022111, 28231629, 36367086, 98671659, 132798279, 163143714, 201713946, 251860911, 434246667, 537424773, 968870877, 999640581, 1495625721, 1548129363, 3338717307, 3836384682, 6316358811, 6982412973 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A120944.

LINKS

Table of n, a(n) for n=1..26.

EXAMPLE

Prime factors of 28101 are 3, 17, 19, 29 and tau(28101) = 16, phi(28101) = 16128. 28101 - 16128 = 11973 and  11973 / (3 - 16) = -921, 11973 / (17 - 16) = 11973, 11973 / (19 - 16) = 3991, 11973 / (29 - 16) = 921.

MAPLE

with (numtheory); P:=proc(q) global a, b, c, i, ok, p, n;

for n from 2 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;

for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=tau(n) then ok:=0; break;

else if not type((n-phi(n))/(a[i][1]-tau(n)), integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(6*10^9);

CROSSREFS

Cf. A000005, A000010, A228299-A228302, A229274-A229276, A229321, A229322, A229324.

Sequence in context: A333747 A124000 A229321 * A068443 A113940 A315280

Adjacent sequences:  A229320 A229321 A229322 * A229324 A229325 A229326

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Sep 20 2013

EXTENSIONS

a(9)-a(27) from Giovanni Resta, Sep 20 2013

First term deleted by Paolo P. Lava, Sep 23 2013

STATUS

approved

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Last modified May 17 23:07 EDT 2022. Contains 353779 sequences. (Running on oeis4.)