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A344702 Positions k where A344695(k) is not multiplicative.

%I A344702 #16 Mar 03 2024 09:04:22
%S A344702 108,196,200,216,288,432,441,500,540,588,600,675,676,756,784,800,864,
%T A344702 882,980,1000,1080,1125,1188,1225,1323,1350,1372,1400,1404,1440,1444,
%U A344702 1500,1512,1521,1568,1728,1764,1800,1836,2000,2016,2028,2052,2156,2160,2200,2205,2250,2352,2376,2400,2450,2484,2548,2592,2600
%N A344702 Positions k where A344695(k) is not multiplicative.
%C A344702 Numbers k with a factorization into coprime x and k/x with A344695(x) * A344695(k/x) <> A344695(k). - _Peter Munn_, Jun 04 2021
%e A344702 For 108 = 4*27, A344695(108) = 8, although A344695(4) = 1 and A344695(27) = 4, and 1*4 != 8, therefore 108 is included in this sequence.
%e A344702 For 441 = 9*49, A344695(441) = 3, although A344695(9) = 1 and A344695(49) = 1, and 1*1 != 3, therefore 441 is included in this sequence.
%o A344702 (PARI)
%o A344702 A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
%o A344702 A344695(n) = gcd(sigma(n), A001615(n));
%o A344702 A344695mult(n) = { my(f = factor(n)); prod(k=1, #f~, A344695(f[k, 1]^f[k, 2])); };
%o A344702 isA344702(n) = (A344695(n)!=A344695mult(n));
%Y A344702 Cf. A000203, A001615, A344695, A344696, A344697.
%Y A344702 Subsequence of A013929 and of A024619.
%K A344702 nonn
%O A344702 1,1
%A A344702 _Antti Karttunen_, May 27 2021