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Numbers k such that (Sum of totatives of k) == 1 (mod Sum of primes dividing k with multiplicity).
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%I #9 Jan 03 2021 19:46:23

%S 2,6,40,45,90,420,468,608,741,873,1216,1547,2425,2451,2829,4199,4208,

%T 6384,6916,7552,7667,8250,8325,8815,8820,11008,11765,12348,12408,

%U 12711,13377,13920,14157,15065,15246,15738,16836,17640,17690,18020,18791,19551,19572,22161,22790,23040,23856,24681

%N Numbers k such that (Sum of totatives of k) == 1 (mod Sum of primes dividing k with multiplicity).

%H Robert Israel, <a href="/A340299/b340299.txt">Table of n, a(n) for n = 1..2000</a>

%F k such that A023896(k) == 1 (mod A001414(k)).

%e a(3) = 40 is a term because A023896(40) = 320, A001414(40) = 11, and 320 == 1 (mod 11).

%p filter:= proc(n) local F, t;

%p F:= ifactors(n)[2];

%p n*mul((t[1]-1)*t[1]^(t[2]-1), t=F)/2 mod add(t[1]*t[2], t=F) = 1;

%p end proc:

%p select(filter, [$2..50000]);

%Y Cf. A001414, A023896, A340297.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 03 2021