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A171256 Numbers n such that sigma(n) = 10*phi(n) (where sigma=A000203, phi=A000010).

%I A171256 #21 Jul 29 2024 19:02:17
%S A171256 168,270,570,2376,2436,5016,6426,7110,13566,15834,34452,58520,62568,
%T A171256 72732,75210,113832,126882,168756,169218,191862,199368,223938,240312,
%U A171256 280488,308568,321468,420888,449442,472758,661848,673608,776736,848540,854496,907236
%N A171256 Numbers n such that sigma(n) = 10*phi(n) (where sigma=A000203, phi=A000010).
%C A171256 If n is in this sequence, then for any prime p not dividing n, sigma(np) - 10*phi(np) = 2*sigma(n).
%H A171256 Amiram Eldar, <a href="/A171256/b171256.txt">Table of n, a(n) for n = 1..10000</a> (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)
%H A171256 Kevin A. Broughan and Daniel Delbourgo, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Broughan/broughan26.html">On the Ratio of the Sum of Divisors and Euler’s Totient Function I</a>, Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8.
%H A171256 Kevin A. Broughan and Qizhi Zhou, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Broughan/bro32.html">On the Ratio of the Sum of Divisors and Euler's Totient Function II</a>, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2.
%t A171256 Select[Range[10^6], DivisorSigma[1, #] == 10 * EulerPhi[#] &] (* _Amiram Eldar_, Dec 04 2019 *)
%o A171256 (PARI) for(k=1,10^6, sigma(k) - 10*eulerphi(k) || print1(k", "));
%Y A171256 Cf. A062699, A068391, A074400, A068390, A136547, A104900, A136540, A104901, A163667, A171257, A104902, A171258, A171259, A171260, A104903.
%K A171256 nonn
%O A171256 1,1
%A A171256 _M. F. Hasler_, Mar 19 2010