cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A275384 Composite squarefree numbers such that the arithmetic mean of its prime factors is an integer.

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%I A275384 #13 Feb 25 2021 08:31:38
%S A275384 15,21,33,35,39,42,51,55,57,65,69,77,78,85,87,91,93,95,105,110,111,
%T A275384 114,115,119,123,129,133,141,143,145,155,159,161,170,177,183,185,186,
%U A275384 187,195,201,203,205,209,213,215,217,219,221,222,230,231,235,237,247,249,253,258,259,265,267
%N A275384 Composite squarefree numbers such that the arithmetic mean of its prime factors is an integer.
%C A275384 Sopf(a(n)) is multiple of omega(a(n)) (sopf(n) is the sum of the distinct prime factors of n, and omega(n) is the number of distinct primes dividing n).
%C A275384 This sequence is subsequence of A078177 and supersequence of A187073.
%H A275384 Amiram Eldar, <a href="/A275384/b275384.txt">Table of n, a(n) for n = 1..10000</a>
%e A275384 170 is in the sequence because 170 = 17*2*5 (squarefree number) and (17+2+5)/3 = 8 is an integer.
%t A275384 Select[Range@ 270, And[CompositeQ@ #, SquareFreeQ@ #, IntegerQ@ Mean@ FactorInteger[#][[All, 1]]] &] (* _Michael De Vlieger_, Jul 25 2016 *)
%o A275384 (PARI) sopf(n)= my(f, s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); s
%o A275384 for(i=2,500,if(issquarefree(i)&&!isprime(i),m=sopf(i)/omega(i);if(m==truncate(m),print1(i,", "))))
%Y A275384 Cf. A005117, A078177, A134344, A187073, A229094.
%K A275384 nonn
%O A275384 1,1
%A A275384 _Antonio Roldán_, Jul 25 2016