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A343142 a(n) = sqrt(k*A001414(k)+1) for k in A343141. 1

%I

%S 7,11,19,23,41,41,71,103,113,151,223,199,239,199,241,307,487,379,491,

%T 419,1063,1777,1013,881,1741,2339,1409,3169,1597,2287,1471,2143,5009,

%U 2521,5393,2351,3389,2393,2663,2161,2887,2969,4271,3361,4889,2549,10177,3191,3499,16631,2753,10243,4481,3691

%N a(n) = sqrt(k*A001414(k)+1) for k in A343141.

%C Primes that occur more than once in the sequence include 41, 199, 4159, 9437, 10687, 16561, 31249, 40591, 64601, 67339, 91631, 93889, 96799, 111871, 122201, 145417, 180847, 911201.

%H Robert Israel, <a href="/A343142/b343142.txt">Table of n, a(n) for n = 1..450</a>

%F a(n) = sqrt(A343141(n)*A001414(A343141(n))+1).

%e a(3) = 19 because A343141(3) = 36 and sqrt(36*A001414(36)+1) = 19.

%p sopf:= proc(x) local t; add(t[1]*t[2],t=ifactors(x)[2]) end proc:

%p g:= proc(n) local x,y;

%p x:= n*sopf(n)+1;

%p if issqr(x) then

%p y:= sqrt(x);

%p if isprime(y) then return y fi

%p fi

%p end proc:

%p map(g, [$1..10^5]);

%t Block[{f}, f[n_] := Sqrt[n*Total@ Flatten[ConstantArray @@@ FactorInteger[n]] + 1]; f /@ Select[Range[200000], PrimeQ@ f[#] &] ] (* _Michael De Vlieger_, Apr 06 2021 *)

%Y Cf. A001414, A343141.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Apr 06 2021

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Last modified September 24 10:21 EDT 2021. Contains 347636 sequences. (Running on oeis4.)