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.

A266618 Least number whose arithmetic mean of all prime factors, counted with multiplicity, is equal to n.

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%I A266618 #32 Feb 22 2016 04:22:38
%S A266618 2,3,15,5,35,7,39,65,51,11,95,13,115,161,87,17,155,19,111,185,123,23,
%T A266618 215,141,235,329,159,29,371,31,183,305,427,201,335,37,219,365,511,41,
%U A266618 395,43,415,524,267,47,623,1501,291,485,303,53,515,321,327,545,339,59
%N A266618 Least number whose arithmetic mean of all prime factors, counted with multiplicity, is equal to n.
%C A266618 Obviously a(p) = p if p is prime.
%C A266618 Similar to A082572 but here the prime factors are not necessarily distinct. First difference for a(45) = 524 while A082572(45) = 581.
%H A266618 Paolo P. Lava, <a href="/A266618/b266618.txt">Table of n, a(n) for n = 2..1000</a>
%e A266618 Prime factor of 15 are 3 and 5: (3 + 5) / 2 = 4 and no other number less than 15 has arithmetic mean of all its prime factors, counted with multiplicity, equal to 4.
%p A266618 with(numtheory): P:= proc(q) local a,b,i,k,n; for i from 2 to q do
%p A266618 for n from 2 to q do a:=ifactors(n)[2]; b:=add(a[k][1]*a[k][2],k=1..nops(a))/add(a[k][2],k=1..nops(a));
%p A266618 if type(b,integer) then if i=b then lprint(b,n); break; fi; fi; od; od; end: P(10^9);
%o A266618 (PARI) ampf(n) = my(f = factor(n)); (sum(k=1, #f~, f[k,1]*f[k,2]) / vecsum(f[,2]));
%o A266618 a(n) = {m = 2; while (ampf(m) != n, m++); m;} \\ _Michel Marcus_, Feb 22 2016
%Y A266618 Cf. A078177, A082572, A200612.
%K A266618 nonn
%O A266618 2,1
%A A266618 _Paolo P. Lava_, Feb 22 2016