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 A247213 Numbers n = Product_(p_i^e_i) such that nn = Product_((p_i + 2)^e_i) is divisible by n. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 7 03:39 EDT 2024. Contains 375008 sequences. (Running on oeis4.)