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A226113 Composite squarefree numbers n such that the ratio (n - 1/3)/(p(i) + 1/3) is an integer, where p(i) are the prime factors of n. 2
773227, 13596427, 26567147, 140247467, 525558107, 1390082027, 1847486667, 2514565387, 3699765755, 4060724267, 4520219947, 6185512667, 6480142667, 8328046827, 9951353867, 10268992067, 11720901387, 14149448387, 14913513067, 21926400427, 22367433387, 24260249387 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also composite squarefree numbers n such that (3*p(i)+1) | (3*n-1).

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..77 (terms < 2*10^12)

EXAMPLE

The prime factors of 773227 are 7, 13, 29 and 293. We see that (773227 - 1/3)/(7 + 1/3) = 231968, (773227 - 1/3)/(13 + 1/3) = 57992, (773227 - 1/3)/(29 + 1/3) = 26360 and (773227 - 1/3)/(293 + 1/3) = 2636. Hence 773227 is in the sequence.

The prime factors of 1128387 are 3, 13 and 28933. We see that

(1128387 - 1/3)/(3 + 1/3) = 338516, (1128387 - 1/3)/(13 + 1/3) = 84629 but (1128387 - 1/3)/(28933 + 1/3) = 84629/2170. Hence 1128387 is not in the sequence.

MAPLE

with(numtheory); A226113:=proc(i, j) local c, d, n, ok, p;

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

for d from 1 to nops(p) do if p[d][2]>1 or not type((n-j)/(p[d][1]+j), integer) then ok:=0; break; fi; od;

if ok=1 then print(n); fi; fi; od; end: A226113(10^9, 1/3);

CROSSREFS

Cf. A208728, A225702-A225720, A226020, A226111, A226112, A226114.

Sequence in context: A237573 A232123 A232421 * A151562 A023348 A089007

Adjacent sequences:  A226110 A226111 A226112 * A226114 A226115 A226116

KEYWORD

nonn,hard

AUTHOR

Paolo P. Lava, May 29 2013

EXTENSIONS

a(5)-a(22) from Giovanni Resta, Jun 02 2013

STATUS

approved

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Last modified June 26 16:55 EDT 2022. Contains 354885 sequences. (Running on oeis4.)