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A075846 Numbers k such that sopf(k) = (1/2)*(sopf(k+1) + sopf(k-1)), where sopf(x) = sum of the distinct prime factors of x. 8
10, 21, 35, 82, 221, 296, 961, 2665, 12629, 13117, 30317, 54485, 99145, 125750, 132728, 142198, 156379, 185461, 225898, 241057, 265227, 265643, 280918, 281396, 284531, 326698, 379331, 393335, 400685, 437241, 437999, 548101, 584502, 641561 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..100 from Harvey P. Dale)

EXAMPLE

The sum of the distinct prime factors of 21 is 3 + 7 = 10; the sum of the distinct prime factors of 22 is 2 + 11 = 13; the sum of the distinct prime factors of 20 is 2 + 5 = 7; and 10 = (1/2)*(13 + 7). Hence 21 belongs to the sequence.

MATHEMATICA

p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^5], p[ # ] == 0.5 (p[ # + 1] + p[ # - 1]) &]

sopf[n_]:=Total[Transpose[FactorInteger[n]][[1]]]; Rest[Flatten[ Position[ Partition[sopf/@Range[650000], 3, 1], _?(Mean[{First[ #], Last[#]}] == #[[2]]&), {1}, Heads->False]]]+1 (* Harvey P. Dale, Sep 05 2013 *)

PROG

(MAGMA) [k:k in [3..642000]| (1/2)*(&+PrimeDivisors(k+1) + &+PrimeDivisors(k-1)) eq (&+PrimeDivisors(k))]; // Marius A. Burtea, Feb 12 2020

CROSSREFS

Cf. A008472, A075565, A075784, A076525, A076527, A076531, A076532, A076533.

Sequence in context: A051942 A250664 A082581 * A164714 A324600 A240536

Adjacent sequences:  A075843 A075844 A075845 * A075847 A075848 A075849

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Oct 18 2002

EXTENSIONS

Edited and extended by Ray Chandler, Feb 13 2005

STATUS

approved

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Last modified September 19 21:11 EDT 2021. Contains 347564 sequences. (Running on oeis4.)