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A029591 For n>0, a(n) is the least quasi-Carmichael number to base -n, extended to n=0 with the least composite squarefree integer. 7
6, 399, 598, 165, 1886, 715, 148219, 273, 343027, 231, 935, 3445, 4681203, 1547, 2821, 1105, 21098, 43183, 258482, 27071, 2117473, 3059, 10373, 2737, 690501, 1595, 23959, 42653, 1621007, 9331, 4169135, 35465, 543973, 14839, 36941, 1885, 4405589, 11063 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is the least squarefree composite integer, for which prime p | a(n) ==> p+n | a(n)+n.

REFERENCES

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 399, p. 89, Ellipses, Paris 2008.

LINKS

Donovan Johnson, Table of n, a(n) for n = 0..250

J.-M. De Koninck, Those fascinating numbers, Entry 399, AMS, 2009.

Index entries for sequences related to Carmichael numbers.

EXAMPLE

For n=6 the minimum is a(n)=148219. Prime factors of 148219 are 19, 29 and 269. We have 148219 + 6 = 148225, 19 + 6 = 25 and 148225 / 25 = 5929, 29 + 6 = 35 and 148225 / 35 = 4235, 269 + 6 = 275 and 148225 / 275 = 539. - Paolo P. Lava, Aug 09 2013

MAPLE

with(numtheory); P:=proc(i) local d, k, n, ok, p; for k from 0 to i do

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 then ok:=0; break; fi;

if  not type((n+k)/(p[d][1]+k), integer) then ok:=0; break; fi; od;

if ok=1 then print(n); break; fi; fi; od; od; end: P(10^9); # Paolo P. Lava, Aug 09 2013

PROG

(PARI) a(n) = {forcomposite (k=1, oo, if (issquarefree(k) && (omega(k) >= 2), my(f=factor(k)[, 1]); my(ok = 1); for (j=1, #f, if ((k+n) % (f[j]+n), ok = 0; break); ); if (ok, return (k)); ); ); } \\ Michel Marcus, Jan 09 2020

CROSSREFS

Cf. A029590 (base n), A257750 (quasi-Carmichael numbers).

Sequence in context: A058807 A000474 A291593 * A151578 A172227 A331352

Adjacent sequences:  A029588 A029589 A029590 * A029592 A029593 A029594

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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