A328461 a(n) = A276156(n) / A002110(A007814(n)).

1, 1, 3, 1, 7, 4, 9, 1, 31, 16, 33, 6, 37, 19, 39, 1, 211, 106, 213, 36, 217, 109, 219, 8, 241, 121, 243, 41, 247, 124, 249, 1, 2311, 1156, 2313, 386, 2317, 1159, 2319, 78, 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

Offset: 1

Author

Antti Karttunen, Oct 16 2019

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

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

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

Cf. A328471, A328472, A328473, A328474.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
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); };
A328461(n) = (A276156(n)/A002110(valuation(n,2)));

Formula

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

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