A271874 Smallest base-n Fermat pseudoprime with n distinct prime factors.

341, 286, 11305, 2203201, 12306385, 9073150801, 3958035081, 2539184851126, 152064312120721, 10963650080564545, 378958695265110961, 1035551157050957605345, 57044715596229144811105, 6149883077429715389052001, 426634466310819456228926101, 166532358913107245358261399361

Offset

2,1

Comments

Main diagonal of A271873.

Links

Daniel Suteu, Table of n, a(n) for n = 2..27

Example

a(4) = 11305, since 11305 is the smallest term x of A020136 such that A001221(x) = 4.

Prog

(PARI) a(n) = forcomposite(c=1, , if(Mod(n, c)^(c-1)==1, if(omega(c)==n, return(c))))
(PARI)
fermat_psp(A, B, k, base) = A=max(A, vecprod(primes(k))); (f(m, l, p, j) = my(list=List()); forprime(q=p, sqrtnint(B\m, j), if(base%q != 0, my(v=m*q, t=q, r=nextprime(q+1)); while(v <= B, my(L=lcm(l, znorder(Mod(base, t)))); if(gcd(L, v) == 1, if(j==1, if(v>=A && if(k==1, !isprime(v), 1) && (v-1)%L == 0, listput(list, v)), if(v*r <= B, list=concat(list, f(v, L, r, j-1)))), break); v *= q; t *= q))); list); vecsort(Vec(f(1, 1, 2, k)));
a(n) = if(n < 2, return()); my(x=vecprod(primes(n)), y=2*x); while(1, my(v=fermat_psp(x, y, n, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ Daniel Suteu, Sep 02 2022

Crossrefs

Cf. A001221, A020136, A271873.

Sequence in context: A271801 A322120 A250199 * A025335 A025327 A101852

Adjacent sequences: A271871 A271872 A271873 * A271875 A271876 A271877

Keyword

nonn

Author

Felix Fröhlich, Apr 16 2016

Extensions

a(7)-a(17) from Daniel Suteu, Sep 02 2022

Status

approved