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a(n) = A276156(n) / A002110(A007814(n)).
13

%I #17 Oct 18 2019 21:28:48

%S 1,1,3,1,7,4,9,1,31,16,33,6,37,19,39,1,211,106,213,36,217,109,219,8,

%T 241,121,243,41,247,124,249,1,2311,1156,2313,386,2317,1159,2319,78,

%U 2341,1171,2343,391,2347,1174,2349,12,2521,1261,2523,421,2527,1264,2529,85,2551,1276,2553,426,2557,1279,2559,1,30031,15016,30033,5006

%N a(n) = A276156(n) / A002110(A007814(n)).

%C 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. In this sequence that sum is then divided by the largest primorial that divides it, which only depends on the position of the least significant 1-bit in the binary expansion of the original n, that is, the 2-adic valuation of n.

%H Antti Karttunen, <a href="/A328461/b328461.txt">Table of n, a(n) for n = 1..8192</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) = A276156(n) / A002110(A007814(n)).

%F a(n) = A111701(A276156(n)).

%o (PARI)

%o A002110(n) = prod(i=1,n,prime(i));

%o 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 A328461(n) = (A276156(n)/A002110(valuation(n,2)));

%Y Cf. A000265, A002110, A007814, A111701, A276154, A276156.

%Y Cf. A328462 (bisection, also row 1 of array A328464 which shows the same information in tabular form).

%Y Cf. A328471, A328472, A328473, A328474.

%K nonn

%O 1,3

%A _Antti Karttunen_, Oct 16 2019