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A229322 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
72285, 82218, 1612671, 52371129, 511130199, 2111850465, 4789685289, 8884216243, 8916435021, 9863075721, 15364177629, 28243714821, 99459827349 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(15) > 10^11. - Giovanni Resta, Sep 20 2013

Subsequence of A120944.

LINKS

Table of n, a(n) for n=1..13.

EXAMPLE

Prime factors of 82218 are 2, 3, 71, 193 and tau(82218) = 16, phi(82218) = 26680. 82218 + 26680 = 109098 and  109098 / (2 + 16) = 6061, 109098 / (3 + 16) = 5742, 109098 / (71 + 16) = 1254, 109098 / (193 + 16) = 522.

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 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, A229323, A229324.

Sequence in context: A254911 A254904 A257206 * A269320 A126658 A251340

Adjacent sequences:  A229319 A229320 A229321 * A229323 A229324 A229325

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Sep 20 2013

EXTENSIONS

a(4)-a(14) 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 23 18:08 EDT 2022. Contains 353993 sequences. (Running on oeis4.)