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Numbers k such that k divides A353790(k), where A353790(n) = phi(A003973(n)) * A064989(A003973(n)).
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%I #12 May 12 2022 17:36:54

%S 1,2,4,8,12,24,36,44,72,96,112,128,132,160,180,220,288,336,352,360,

%T 384,396,480,528,560,640,660,880,1044,1056,1152,1232,1344,1404,1440,

%U 1680,1760,1920,1980,2088,2352,2376,2464,2496,2640,3168,3600,3696,3920,4032,4400,4736,5220,5280,5376,5760,5824,6075,6144,6160

%N Numbers k such that k divides A353790(k), where A353790(n) = phi(A003973(n)) * A064989(A003973(n)).

%C Of 5263 initial terms (terms < 2^32), only 67 are odd, and of these, only two, 1 and 1525391261 (= 503^2 * 6029) are in A007310. Of 5263 initial terms, 4653 are multiples of 3, 2331 are multiples of 81, and 3780 are multiples of 5.

%H Antti Karttunen, <a href="/A353796/b353796.txt">Table of n, a(n) for n = 1..5263; 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 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%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 A353790(n) = { my(s=sigma(A003961(n))); (eulerphi(s)*A064989(s)); };

%o isA353796(n) = !(A353790(n)%n);

%Y Cf. A000010, A000203, A003961, A003973, A353790, A353797 (subsequence).

%Y Cf. also A353795.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 12 2022