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

1,3

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

Formula

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

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

Prog

(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)));

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.

Sequence in context: A283764 A010603 A269423 * A341494 A210198 A271258

Adjacent sequences: A328458 A328459 A328460 * A328462 A328463 A328464

Keyword

nonn

Author

Antti Karttunen, Oct 16 2019

Status

approved