cp's OEIS Frontend

A353797 Numbers k such that k*A003557(A003961(k)) divides A353790(k), where A353790(n) = phi(A003973(n)) * A064989(A003973(n)).

%I A353797 #13 May 12 2022 17:36:59
%S A353797 1,2,4,44,132,220,396,660,1980,3920,4400,8800,11484,13200,13328,22000,
%T A353797 26400,30800,39984,57420,66640,74800,92400,119952,149600,199920,
%U A353797 224400,269892,277200,448800,523600,599760,673200,771012,1063692,1345792,1346400,1570800,3478608,4037376,4712400,5664400,6344448,8038800,10574080
%N A353797 Numbers k such that k*A003557(A003961(k)) divides A353790(k), where A353790(n) = phi(A003973(n)) * A064989(A003973(n)).
%C A353797 Note that A003557(A003961(n)) [= A003961(A003557(n))] is a divisor of A003972(n), therefore the set of k such that A353789(k) divides A353790(k) is a subset of this sequence.
%C A353797 Of 101 initial terms (terms < 2^32) all others apart from a(1) = 1 and a(2) = 2 are multiples of 4.
%H A353797 Antti Karttunen, <a href="/A353797/b353797.txt">Table of n, a(n) for n = 1..101; all terms <= 2^32</a>
%H A353797 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A353797 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A353797 (PARI)
%o A353797 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A353797 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A353797 A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
%o A353797 A353790(n) = { my(s=sigma(A003961(n))); (eulerphi(s)*A064989(s)); };
%o A353797 isA353797(n) = !(A353790(n)%(n*A003557(A003961(n))));
%Y A353797 Subsequence of A353796.
%Y A353797 Cf. A000010, A000203, A003557, A003961, A003972, A003973, A353789, A353790.
%K A353797 nonn
%O A353797 1,2
%A A353797 _Antti Karttunen_, May 12 2022