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A324111 Numbers n for which A324108(n) = A324054(n-1) and which are neither prime powers nor of the form 2^i * p^j, where p is an odd prime, with either exponent i or j > 0.

%I A324111 #14 Feb 16 2019 20:39:46
%S A324111 1,87,174,348,696,1392,2091,2784,4182,5568,8364,11136,16683,16728,
%T A324111 22272,33215,33366,33456,44544,66430,66732,66912,89088,132860,133464,
%U A324111 133824,178176,265720,266928,267179,267648,356352,531440,533856,534358,535296,712704,1062880,1066877,1067712,1068716,1070592,1319235,1425408
%N A324111 Numbers n for which A324108(n) = A324054(n-1) and which are neither prime powers nor of the form 2^i * p^j, where p is an odd prime, with either exponent i or j > 0.
%C A324111 Setwise difference of A324109 and A070776.
%C A324111 Setwise difference of A070537 and A324110.
%C A324111 If an odd number n > 1 is present, then all 2^k * n are present also. Odd terms > 1 are given in A324112.
%H A324111 Antti Karttunen, <a href="/A324111/b324111.txt">Table of n, a(n) for n = 1..173</a>
%e A324111 87 is a term, as 87 = 3*29, A324054(3-1) = 4, A324054(29-1) = 156, and A324108(87) = 4*156 = 624 = A324054(87-1).
%o A324111 (PARI)
%o A324111 A000265(n) = (n/2^valuation(n, 2));
%o A324111 A324054(n) = { my(p=2,mp=p*p,m=1); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, if(3==(n%4),mp *= p,m *= (mp-1)/(p-1))); n>>=1); (m); };
%o A324111 A324108(n) = { my(f=factor(n)); prod(i=1, #f~, A324054((f[i,1]^f[i,2])-1)); };
%o A324111 isA324111(n) = ((1!=omega(n))&&(1!=omega(A000265(n)))&&(A324054(n-1)==A324108(n)));
%o A324111 for(n=1,2^20,if(isA324111(n), print1(n,", ")))
%Y A324111 Cf. A070537, A070776, A324109, A324110, A324112.
%K A324111 nonn
%O A324111 1,2
%A A324111 _Antti Karttunen_, Feb 15 2019