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A345946 Prime powers k that have such a proper divisor d for which A002034(d) = A002034(k).

%I A345946 #15 Jul 07 2021 10:32:18
%S A345946 8,64,81,128,1024,6561,8192,15625,16384,32768,262144,531441,1594323,
%T A345946 2097152,4194304,5764801,33554432,129140163,244140625,268435456,
%U A345946 536870912,1073741824,2147483648,10460353203,17179869184,137438953472,274877906944,847288609443,2199023255552
%N A345946 Prime powers k that have such a proper divisor d for which A002034(d) = A002034(k).
%C A345946 Numbers k such that A345950(k) = 0 (or equivalently, A345935(k) > 1), and A010055(k) = 1.
%H A345946 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%e A345946 8 = 2^3 is present because A002034(8) = 4 = A002034(4).
%o A345946 (PARI)
%o A345946 A002034(n) = if(1==n,n,my(s=factor(n)[, 1], k=s[#s], f=Mod(k!, n)); while(f, f*=k++); (k)); \\ After code in A002034.
%o A345946 A345950(n) = { my(x=A002034(n)); fordiv(n,d,if(A002034(d)==x,return(d==n))); };
%o A345946 isA345946(n) = (!isprime(n) && isprimepower(n) && !A345950(n));
%Y A345946 Cf. A002034, A010055, A345935, A345950.
%Y A345946 Intersection of A000961 and A345945.
%K A345946 nonn
%O A345946 1,1
%A A345946 _Antti Karttunen_, Jul 04 2021
%E A345946 More terms from _Jinyuan Wang_, Jul 07 2021