A328473 - OEIS

A328473

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

0, 0, 2, 0, 6, 6, 8, 0, 30, 30, 32, 30, 36, 36, 38, 0, 210, 210, 212, 210, 216, 216, 218, 210, 240, 240, 242, 240, 246, 246, 248, 0, 2310, 2310, 2312, 2310, 2316, 2316, 2318, 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

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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. 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.

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

FORMULA

a(n) = A276156(A129760(n)).

a(n) = A276151(A276156(n)) = A276156(n) - A002110(A007814(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); };

A328473(n) = (A276156(n)-A002110(valuation(n, 2)));