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A287514 Squarefree numbers n such that alpha(n) = lambda(n), where alpha(n) = LCM of all (p+1) for primes p dividing n, and lambda(n) = A002322(n). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Are there infinitely many such numbers?

These numbers have at least three prime factors.

If m and n are in the sequence, then lcm(m,n) 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

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Last modified November 13 01:54 EST 2019. Contains 329085 sequences. (Running on oeis4.)