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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
4, 16, 35, 65, 77, 78, 114, 146, 161, 185, 209, 221, 256, 335, 341, 371, 377, 437, 485, 515, 595, 611, 626, 644, 654, 671, 707, 731, 767, 779, 805, 851, 899, 917, 965, 1007, 1067, 1115, 1157, 1211, 1247, 1271, 1309, 1337, 1385, 1397, 1463, 1495, 1529, 1535, 1577, 1631, 1645, 1691, 1771 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..55.

F. Luca and C. Pomerance, Local behavior of the composition of the aliquot and co-totient functions

EXAMPLE

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

MATHEMATICA

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 *)

PROG

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

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

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

CROSSREFS

Cf. A000203, A001065, A033632, A051953.

Sequence in context: A101653 A043100 A078714 * A104125 A014727 A174597

Adjacent sequences:  A292205 A292206 A292207 * A292209 A292210 A292211

KEYWORD

nonn

AUTHOR

Altug Alkan, Sep 11 2017

STATUS

approved

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Last modified March 20 07:42 EDT 2019. Contains 321345 sequences. (Running on oeis4.)