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A292208 Composite numbers n such that sigma(cototient(n)) = cototient(sigma(n) - n) + cototient(n); that is, f(g(n)) = g(f(n)) where f = A001065 and g = A051953. 1

%I

%S 4,16,35,65,77,78,114,146,161,185,209,221,256,335,341,371,377,437,485,

%T 515,595,611,626,644,654,671,707,731,767,779,805,851,899,917,965,1007,

%U 1067,1115,1157,1211,1247,1271,1309,1337,1385,1397,1463,1495,1529,1535,1577,1631,1645,1691,1771

%N Composite numbers n such that sigma(cototient(n)) = cototient(sigma(n) - n) + cototient(n); that is, f(g(n)) = g(f(n)) where f = A001065 and g = A051953.

%C Luca and Pomerance proved that arithmetic functions f(g(n)) and g(f(n)) are independent where f = A001065 and g = A051953. For related details and theorems see Luca & Pomerance link.

%H F. Luca and C. Pomerance, <a href="https://math.dartmouth.edu/~carlp/alicot5.pdf">Local behavior of the composition of the aliquot and co-totient functions</a>

%e 35 = 5*7 is a term because A001065(A051953(35)) = A051953(A001065(35)).

%t Select[Range@ 1800, Function[n, And[CompositeQ@ n, DivisorSigma[1, n - EulerPhi@ n] == (n - EulerPhi@ n) + # - EulerPhi@ # &[DivisorSigma[1, n] - n]]]] (* _Michael De Vlieger_, Sep 12 2017 *)

%o (PARI) a001065(n) = sigma(n)-n;

%o a051953(n) = n-eulerphi(n);

%o lista(nn) = forcomposite(n=4, nn, if(a051953(a001065(n))==a001065(a051953(n)), print1(n, ", ")));

%Y Cf. A000203, A001065, A033632, A051953.

%K nonn

%O 1,1

%A _Altug Alkan_, Sep 11 2017

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Last modified April 25 18:12 EDT 2019. Contains 322461 sequences. (Running on oeis4.)