A247213 Numbers n = Product_(p_i^e_i) such that nn = Product_((p_i + 2)^e_i) is divisible by n.

1, 2, 4, 8, 16, 32, 64, 105, 128, 210, 256, 315, 420, 512, 630, 840, 1024, 1260, 1575, 1680, 2048, 2520, 3150, 3360, 4096, 5040, 6300, 6720, 8192, 10080, 11025, 12600, 13440, 16384, 20160, 22050, 25200, 26880, 32768, 33075, 40320, 44100, 50400, 53760, 65536

Offset

1,2

Comments

That is, numbers n, such that A166590(n) is divisible by n.

A000079, powers of 2, is a subsequence.

Thomas Ordowski remarks that the only squarefrees of this sequence are: 1, 2, 105, and 210.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..164

Example

A166590(2)=4 is divisible by 2, so 2 is in the sequence.
A166590(105) = A166590(3*5*7) = 5*7*9 = 3*(3*5*7), so 105 is in the sequence.

Mathematica

a247213[n_] := Select[Range@n, Mod[Times @@ Power @@@ Transpose[{Plus[First /@ FactorInteger@#, 2], Last /@ FactorInteger@#}], #] == 0 &]; a247213[2^16] (* Michael De Vlieger, Jan 07 2015 *)

Prog

(PARI) isok(n) = { f = factor(n); for (i=1, #f~, f[i, 1] += 2); newn = factorback(f);  newn % n == 0; }
(Python)
from operator import mul
from functools import reduce
from sympy import factorint
A247213_list = [n for n in range(1, 10**4) if n <= 1 or not reduce(mul, [(p+2)**e for p, e in factorint(n).items()]) % n]
# Chai Wah Wu, Jan 05 2015

Crossrefs

Cf. A000079, A166590.

Sequence in context: A008881 A208743 A335853 * A302934 A069050 A343844

Adjacent sequences: A247210 A247211 A247212 * A247214 A247215 A247216

Keyword

nonn

Author

Michel Marcus, after a suggestion from Thomas Ordowski, Nov 26 2014

Status

approved