%I #32 May 25 2022 09:13:21

%S 1,3,15,45,175,357,585,608,646,962,1071,1292,1443,1508,1586,1664,1665,

%T 1898,2275,2295,2379,2745,2847,3285,3848,4082,4329,4514,4641,4736,

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

%D S. W. Golomb, Equality among number-theoretic functions, Manuscript, no date; Second update, Dec 29, 1992.

%H Antti Karttunen, <a href="/A260021/b260021.txt">Table of n, a(n) for n = 1..20000</a>

%H S. W. Golomb, <a href="/A006872/a006872_1.pdf">Equality among number-theoretic functions</a>, Unpublished manuscript. (Annotated scanned copy)

%H Antti Karttunen, <a href="/A260021/a260021.txt">Data supplement: n, a(n) computed for n = 1..103800</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F {k | 1==A353637(k) and 0==A354344(k)}. - _Antti Karttunen_, May 25 2022

%o (PARI)

%o 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 A353637(n) = (eulerphi(sigma(n))==eulerphi(n));

%o isA260021(n) = (A353637(n) && !A354344(n)); \\ _Antti Karttunen_, May 24 2022

%Y Setwise difference A006872 \ A354345. Subset of positions of zeros in A353636.

%Y Cf. A354362 (subsequence).

%Y Cf. also A005383, A353637, A354344.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jul 14 2015

%E Term a(1) = 1 prepended and terms a(14) .. a(56) added by _Antti Karttunen_, May 24 2022