cp's OEIS Frontend

A324348 a(n) = A294898(A005940(1+n)), where A294898(k) = A005187(k) - A000203(k).

%I A324348 #8 Feb 24 2019 17:52:51
%S A324348 0,0,0,0,2,-2,3,0,3,0,2,-6,16,-5,10,0,7,1,7,-4,19,-16,8,-14,38,4,22,
%T A324348 -21,88,-16,38,0,9,5,16,-3,33,-15,16,-12,54,-7,14,-52,96,-58,26,-30,
%U A324348 104,22,62,-20,142,-76,43,-53,280,26,119,-68,464,-42,116,0,14,7,18,1,44,-14,38,-11,65,-1,38,-59,174,-66,52,-28,113,16,72,-59,191,-160,0,-124
%N A324348 a(n) = A294898(A005940(1+n)), where A294898(k) = A005187(k) - A000203(k).
%C A324348 Positions of zeros is given by the sequence A156552(A295296(n)), n >= 1, sorted into ascending order: 0, 1, 2, 3, 7, 9, 15, 31, 63, 86, 127, 255, 511, 519, 1023, 2047, 4095, 8191, 16383, 32767, ...
%H A324348 Antti Karttunen, <a href="/A324348/b324348.txt">Table of n, a(n) for n = 0..8191</a>
%H A324348 Antti Karttunen, <a href="/A324348/a324348.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%H A324348 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324348 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A324348 a(n) = A294898(A005940(1+n)).
%F A324348 a(n) = A324055(n) - A000120(A005940(1+n)).
%o A324348 (PARI) A324348(n) = { my(m1=2, m2=1, p=2, mp=p*p); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, m1 *= p; if(3==(n%4), mp *= p, m2 *= (mp-1)/(p-1))); n>>=1); ((m1-m2)-hammingweight(m1)); };
%o A324348 (PARI)
%o A324348 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A324348 A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A324348 A294898(n) = (A005187(n) - sigma(n));
%o A324348 A324348(n) = A294898(A005940(1+n));
%Y A324348 Cf. A000120, A000203, A005187, A005940, A294898, A324055.
%Y A324348 Cf. also A156552, A295296, A323248.
%K A324348 sign
%O A324348 0,5
%A A324348 _Antti Karttunen_, Feb 24 2019