cp's OEIS Frontend

A190403 Number n for which sigma(n)=sigma(n'), where sigma is the sum of divisors and n' the arithmetic derivative of n.

%I A190403 #16 Apr 22 2015 10:37:42
%S A190403 4,27,60,84,132,140,204,220,228,260,270,340,372,378,444,492,564,572,
%T A190403 580,620,644,702,708,740,804,812,820,836,860,884,918,945,1026,1068,
%U A190403 1180,1242,1276,1284,1292,1308,1316,1364,1420,1460,1484,1485,1508,1564,1566
%N A190403 Number n for which sigma(n)=sigma(n'), where sigma is the sum of divisors and n' the arithmetic derivative of n.
%H A190403 Nathaniel Johnston, <a href="/A190403/b190403.txt">Table of n, a(n) for n = 1..10000</a>
%p A190403 with(numtheory);
%p A190403 P:=proc(i)
%p A190403 local f,n,p,pfs;
%p A190403 for n from 1 to i do
%p A190403     pfs:=ifactors(n)[2];
%p A190403     f:=n*add(op(2,p)/op(1,p),p=pfs);
%p A190403     if sigma(n)=sigma(f) then print(n); fi;
%p A190403 od;
%p A190403 end:
%p A190403 P(1000);
%t A190403 d[0] = d[1] = 0; d[n_] := n*Total[f = FactorInteger[n]; f[[All, 2]]/f[[All, 1]] ]; Reap[For[n = 1, n < 2000, n++, If[DivisorSigma[1, n] == DivisorSigma[1, d[n]], Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Apr 22 2015 *)
%o A190403 (Python)
%o A190403 from sympy import factorint, totient
%o A190403 A190402 = [n for n in range(2,10**3) if totient(int(sum([n*e/p for p,e in factorint(n).items()]))) == totient(n)] # _Chai Wah Wu_, Aug 21 2014
%Y A190403 Cf. A000203, A003415, A189057, A190402.
%K A190403 nonn,easy
%O A190403 1,1
%A A190403 _Paolo P. Lava_, May 10 2011