A287514 Squarefree numbers k such that alpha(k) = lambda(k), where alpha(k) = LCM of all (p+1) for primes p dividing k, and lambda(k) = A002322(k).

4147, 8294, 8323, 12441, 16646, 20735, 24882, 24969, 41470, 41615, 49938, 55309, 62205, 83230, 91553, 108199, 110618, 124410, 124845, 165927, 183106, 216398, 249690, 274659, 276545, 324597, 331854, 387163, 457765, 540995, 549318, 553090, 608399, 649194, 719017, 774326, 829635, 915530

Offset

1,1

Comments

Are there infinitely many such numbers?

These numbers have at least three prime factors.

If m and k are in the sequence, then lcm(m,k) is in the sequence. - Robert Israel, Jul 05 2017

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..398

Example

4147 = 11*13*29 and lcm(12,14,30) = lcm(10,12,28) = 420.
13*23*29*41*43 multiplied by any divisor of 2*3*5*7*11.

Maple

filter:= proc(n) local F;
  F:= ifactors(n)[2];
  if max(seq(f[2], f=F)) > 1 then return false fi;
ilcm(seq(f[1]-1, f=F)) = ilcm(seq(f[1]+1, f=F))
end proc:
select(filter, [$2..10^6]); # Robert Israel, Jul 05 2017

Mathematica

fQ[n_] := If[ SquareFreeQ@ n, Block[{p = First@ Transpose@ FactorInteger@ n}, LCM @@ (p - 1) == LCM @@ (p + 1)], False]; Select[ Range[10^6], fQ] (* Robert G. Wilson v, Jun 05 2017 *)

Crossrefs

Cf. A002322.

Sequence in context: A254230 A106537 A256080 * A072896 A052464 A161752

Adjacent sequences: A287511 A287512 A287513 * A287515 A287516 A287517

Keyword

nonn

Author

Thomas Ordowski, May 26 2017

Extensions

More terms from Robert G. Wilson v, Jun 05 2017

Status

approved