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A259283 Quasi-Carmichael numbers to at least one positive base. 4
165, 231, 273, 357, 399, 598, 715, 935, 1015, 1105, 1547, 1595, 1885, 1886, 2015, 2093, 2387, 2397, 2451, 2465, 2585, 2679, 2737, 2821, 2915, 3059, 3445, 3913, 3965, 4123, 4991, 5015, 5467, 5719, 6097, 6545, 7055, 7189, 7285, 7553, 7843, 8555, 8569, 8715, 8855 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..2963

EXAMPLE

a(1) = 165 because this is the first squarefree composite number n such that at least one positive integer b except 0 exists such that for every prime factor p of n applies that p+b divides n+b (3): 165=3*5*11 and 6, 8, 14 all divide 168.

PROG

(PARI) for(n=2, 1000000, if(!isprime(n), if(issquarefree(n), f=factor(n); b=0; until(c==0 || b==n, b++; c=0; for(i=1, #f[, 1], if((n+b)%(f[i, 1]+b)>0, c++)); if(c==0, print1(n, ", "))))))

CROSSREFS

Cf. A257750, A257759, A259282.

Sequence in context: A252725 A168355 A083255 * A319502 A270175 A319328

Adjacent sequences:  A259280 A259281 A259282 * A259284 A259285 A259286

KEYWORD

nonn

AUTHOR

Tim Johannes Ohrtmann, Jun 23 2015

STATUS

approved

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Last modified February 27 11:38 EST 2021. Contains 341656 sequences. (Running on oeis4.)