cp's OEIS Frontend

A328473 a(n) = A276156(n) - A002110(A007814(n)).

%I A328473 #9 Oct 18 2019 21:28:05
%S A328473 0,0,2,0,6,6,8,0,30,30,32,30,36,36,38,0,210,210,212,210,216,216,218,
%T A328473 210,240,240,242,240,246,246,248,0,2310,2310,2312,2310,2316,2316,2318,
%U A328473 2310,2340,2340,2342,2340,2346,2346,2348,2310,2520,2520,2522,2520,2526,2526,2528,2520,2550,2550,2552,2550,2556,2556,2558,0,30030
%N A328473 a(n) = A276156(n) - A002110(A007814(n)).
%C A328473 A276156(n) converts the binary expansion of n to a number whose primorial base representation has the same digits of 0's and 1's, thus each one of its terms is a unique sum of distinct primorial numbers. This sequence is otherwise similar, but the primorial number corresponding to the least significant 1-bit of n is dropped from the sum, so the sum is not unique anymore.
%H A328473 Antti Karttunen, <a href="/A328473/b328473.txt">Table of n, a(n) for n = 1..8192</a>
%H A328473 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A328473 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328473 a(n) = A276156(A129760(n)).
%F A328473 a(n) = A276151(A276156(n)) = A276156(n) - A002110(A007814(n)).
%o A328473 (PARI)
%o A328473 A002110(n) = prod(i=1,n,prime(i));
%o A328473 A276156(n) = { my(p=2,pr=1,s=0); while(n,if(n%2,s += pr); n >>= 1; pr *= p; p = nextprime(1+p)); (s); };
%o A328473 A328473(n) = (A276156(n)-A002110(valuation(n,2)));
%Y A328473 Cf. A002110, A053589, A129760, A276151, A276156, A328461, A328474.
%K A328473 nonn,base
%O A328473 1,3
%A A328473 _Antti Karttunen_, Oct 18 2019