cp's OEIS Frontend

A291750 Compound filter: a(n) = P(A003557(n), A048250(n)), where P(n,k) is sequence A000027 used as a pairing function.

%I A291750 #17 Nov 27 2017 19:19:33
%S A291750 1,4,7,8,16,67,29,19,18,154,67,80,92,277,277,53,154,94,191,173,497,
%T A291750 631,277,109,50,862,75,302,436,2557,497,169,1129,1432,1129,142,704,
%U A291750 1771,1541,214,862,4561,947,668,328,2557,1129,179,98,236,2557,905,1432,199,2557,355,3161,4006,1771,2630,1892,4561,564,593,3487,10297,2279,1487,4561,10297,2557
%N A291750 Compound filter: a(n) = P(A003557(n), A048250(n)), where P(n,k) is sequence A000027 used as a pairing function.
%C A291750 A000203 (sigma(n)) is a function of this sequence, because formula
%C A291750   A000203(n) = A092261(n) * A295294(n)
%C A291750 can be rewritten as a relation:
%C A291750   A000203(n) = A000203(A057521(n)) * A048250(n) / A048250(A057521(n)),
%C A291750 where A057521(n) = A064549(A003557(n)), thus A000203(n) is a function of A003557(n) and A048250(n), the values that are packed here into a(n).
%C A291750 A001615 (Dedekind's psi) is a function of this sequence, because it can be written as A001615(n) = A003557(n)*A048250(n).
%H A291750 Antti Karttunen, <a href="/A291750/b291750.txt">Table of n, a(n) for n = 1..10000</a>
%F A291750 a(n) = (1/2)*(2 + ((A003557(n) + A048250(n))^2) - A003557(n) - 3*A048250(n)).
%o A291750 (PARI)
%o A291750 A003557(n) = n/factorback(factor(n)[, 1]); \\ This function from _Charles R Greathouse IV_, Nov 17 2014
%o A291750 A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));
%o A291750 A291750(n) = (1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n));
%Y A291750 Cf. A000027, A000203, A001615, A003557, A048250, A291751 (rgs-version of this filter).
%K A291750 nonn
%O A291750 1,2
%A A291750 _Antti Karttunen_, Sep 04 2017