The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A070005

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A070005

Arithmetic mean of prime factors of n is an integer and n is neither a prime nor power of a prime.
(history; published version)

#13 by N. J. A. Sloane at Sat Mar 28 22:36:04 EDT 2015

STATUS

proposed

approved

#12 by Michel Marcus at Sat Mar 28 03:29:20 EDT 2015

STATUS

editing

proposed

#11 by Michel Marcus at Sat Mar 28 03:29:13 EDT 2015

EXAMPLE

n=33=3.*11, mean=(3+11)/2=6.

STATUS

proposed

editing

#10 by Michel Marcus at Sat Mar 28 03:27:52 EDT 2015

STATUS

editing

proposed

#9 by Michel Marcus at Sat Mar 28 03:27:39 EDT 2015

NAME

Arithmetical Arithmetic mean of prime factors of n is an integer and n is neither a prime nor power of a prime.

PROG

(PARI) lista(nn) = {for (n=2, nn, f = factor(n); if ((#f~ != 1) && (sum(k=1, #f~, f[k, 1]) % #f~ == 0), print1(n, ", ")); ); } \\ Michel Marcus, Mar 28 2015

STATUS

approved

editing

#8 by N. J. A. Sloane at Tue Oct 15 22:31:18 EDT 2013

AUTHOR

_Labos E. (labos(AT)ana.sote.hu), Elemer_, Apr 11 2002

Discussion

Tue Oct 15

22:31

OEIS Server: https://oeis.org/edit/global/2029

#7 by Reinhard Zumkeller at Sat Jun 01 07:29:18 EDT 2013

STATUS

editing

approved

#6 by Reinhard Zumkeller at Sat Jun 01 04:26:03 EDT 2013

PROG

(Haskell)

a070005 n = a070005_list !! (n-1)

a070005_list = filter ((== 0) . a010055) a078174_list

-- Reinhard Zumkeller, Jun 01 2013

CROSSREFS

Cf. A000961, A010055; subsequence of A078174.

#5 by Reinhard Zumkeller at Sat Jun 01 04:24:33 EDT 2013

LINKS

Reinhard Zumkeller, <a href="/A070005/b070005.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#4 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

MATHEMATICA

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] ep[x_] := Table[Part[ffi[x], 2*w], {w, 1, lf[x]}] Do[s=Apply[Plus, ba[n]]/lf[n]; If[IntegerQ[s]&&Greater[lf[n], 1], Print[n]], {n, 2, 1000}]

KEYWORD

easy,nonn,new