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A260021 Solutions to phi(n) = phi(sigma(n)) that are not given by Theorem 3 of Golomb's manuscript.

%I A260021 #32 May 25 2022 09:13:21
%S A260021 1,3,15,45,175,357,585,608,646,962,1071,1292,1443,1508,1586,1664,1665,
%T A260021 1898,2275,2295,2379,2745,2847,3285,3848,4082,4329,4514,4641,4736,
%U A260021 4845,5018,5402,6123,6232,6344,6475,6771,7052,7065,7137,7202,7215,7527,7592,7803,7808,8103,8138,8398,8541,8685,8906,9344,9526,10322
%N A260021 Solutions to phi(n) = phi(sigma(n)) that are not given by Theorem 3 of Golomb's manuscript.
%D A260021 S. W. Golomb, Equality among number-theoretic functions, Manuscript, no date; Second update, Dec 29, 1992.
%H A260021 Antti Karttunen, <a href="/A260021/b260021.txt">Table of n, a(n) for n = 1..20000</a>
%H A260021 S. W. Golomb, <a href="/A006872/a006872_1.pdf">Equality among number-theoretic functions</a>, Unpublished manuscript. (Annotated scanned copy)
%H A260021 Antti Karttunen, <a href="/A260021/a260021.txt">Data supplement: n, a(n) computed for n = 1..103800</a>
%H A260021 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A260021 {k | 1==A353637(k) and 0==A354344(k)}. - _Antti Karttunen_, May 25 2022
%o A260021 (PARI)
%o A260021 A354344(n) = { if(!(n%15),n/=15,if(!(n%9),n/=9,if(!(n%8),n/=8,if(!(n%3),n/=3,if(!(n%2),n/=2,return(0)))))); ((n>5) && isprime(n) && isprime((1+n)/2)); };
%o A260021 A353637(n) = (eulerphi(sigma(n))==eulerphi(n));
%o A260021 isA260021(n) = (A353637(n) && !A354344(n)); \\ _Antti Karttunen_, May 24 2022
%Y A260021 Setwise difference A006872 \ A354345. Subset of positions of zeros in A353636.
%Y A260021 Cf. A354362 (subsequence).
%Y A260021 Cf. also A005383, A353637, A354344.
%K A260021 nonn
%O A260021 1,2
%A A260021 _N. J. A. Sloane_, Jul 14 2015
%E A260021 Term a(1) = 1 prepended and terms a(14) .. a(56) added by _Antti Karttunen_, May 24 2022