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Positions of primes in A351568.
2

%I #7 Feb 25 2022 16:58:28

%S 4,9,12,16,18,20,25,28,44,45,48,50,52,60,63,64,68,72,75,76,80,84,90,

%T 92,99,108,112,116,117,124,126,132,140,148,150,153,156,164,171,172,

%U 175,176,188,192,198,200,204,207,208,212,220,228,234,236,240,244,260,261,268,272,275,276,279,284,288,289,292,304,306

%N Positions of primes in A351568.

%C Numbers k such that A350388(k) is one of the terms of A023194.

%t f[p_, e_] := If[EvenQ[e], (p^(e + 1) - 1)/(p - 1), 1]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[300], PrimeQ[s[#]] &] (* _Amiram Eldar_, Feb 25 2022 *)

%o (PARI)

%o A350388(n) = { my(m=1, f=factor(n)); for(k=1,#f~,if(0==(f[k,2]%2), m *= (f[k,1]^f[k,2]))); (m); };

%o A351568(n) = sigma(A350388(n));

%o isA351575(n) = isprime(A351568(n));

%Y Positions of primes in A351568, positions of ones in A351570.

%Y Cf. A000203, A023194, A350388.

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 24 2022