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Numbers k such that k divides A353794(k), where A353794(n) = A003958(A003973(n)) * A064989(A003973(n)).
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%I #11 May 15 2022 17:21:03

%S 1,4,12,24,36,44,72,96,112,132,180,220,360,384,396,400,480,560,660,

%T 784,832,864,1044,1056,1188,1200,1344,1920,1980,2088,2352,2376,2496,

%U 2800,3168,3600,3920,4320,4736,5220,5280,5376,5824,5940,6800,6912,7056,7200,7488,8400,8800,9504,9900,10000,10440,10800,11484

%N Numbers k such that k divides A353794(k), where A353794(n) = A003958(A003973(n)) * A064989(A003973(n)).

%C Of 2608 initial terms, only 188 are not in A353796. The first three of these are: 400, 784, 832.

%H Antti Karttunen, <a href="/A353795/b353795.txt">Table of n, a(n) for n = 1..2608; all terms <= 2^32</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%o (PARI)

%o A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961

%o A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };

%o A353794(n) = { my(s=sigma(A003961(n))); (A003958(s)*A064989(s)); };

%o isA353795(n) = !(A353794(n)%n);

%Y Cf. A000010, A003958, A003961, A003973, A064989, A353794.

%Y Cf. also A353796.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 12 2022