A382484 Least composite squarefree numbers k > n such that p + n divides k - n, for each prime p dividing k.

385, 182, 195, 1054, 165, 26781, 1015, 4958, 2193, 79222, 5159, 113937, 5593, 160937, 6351, 196009, 3657, 6318638, 2755, 1227818, 12669, 41302, 2795, 152358, 12121, 366821, 21827, 17578, 36569, 12677695, 38335, 457907, 2553, 15334, 141155, 69722351, 1045, 14003, 4823, 2943805

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Example

a(20) = 1227818 = 2 * 19 * 79 * 409 and
  (1227818 - 20) /(2 + 20) = 55809;
  (1227818 - 20) /(19 + 20) = 31482;
  (1227818 - 20) /(79 + 20) = 12402;
  (1227818 - 20) /(409 + 20) = 2862.

Maple

f:= proc(n) local k, F;
      for k from n+1 do
        F:= ifactors(k)[2];
        if nops(F)=1 or F[.., 2] <> [1$nops(F)] then next fi;
        if andmap(p -> (k - n) mod (p+n) = 0, F[.., 1]) then return k fi
      od
end proc:
map(f, [$1..40]); # Robert Israel, Feb 17 2026

Prog

(PARI) isok(k, n) = if (!issquarefree(k) || isprime(k), return(0)); my(f=factor(k)[, 1]); for (i=1, #f, if ((k-n) % (f[i]+n), return(0)); ); return(1);
a(n) = my(k=n+1); while (!isok(k, n), k++); k; \\ Michel Marcus, Mar 30 2025

Crossrefs

Cf. A208728, A225702-A225710, A225711-A225720.

Sequence in context: A254352 A274445 A227974 * A379595 A379983 A069043

Adjacent sequences: A382481 A382482 A382483 * A382485 A382486 A382487

Keyword

nonn

Author

Paolo P. Lava, Mar 29 2025

Extensions

More terms from Michel Marcus, Mar 30 2025

Status

approved