A283985 Sums of distinct terms of A143293: a(n) = Sum_{k>=0} A030308(n,k)*A143293(k).

0, 1, 3, 4, 9, 10, 12, 13, 39, 40, 42, 43, 48, 49, 51, 52, 249, 250, 252, 253, 258, 259, 261, 262, 288, 289, 291, 292, 297, 298, 300, 301, 2559, 2560, 2562, 2563, 2568, 2569, 2571, 2572, 2598, 2599, 2601, 2602, 2607, 2608, 2610, 2611, 2808, 2809, 2811, 2812, 2817, 2818, 2820, 2821, 2847, 2848, 2850, 2851, 2856, 2857, 2859, 2860, 32589

Offset: 0

Author

Antti Karttunen, Mar 19 2017

Keywords

• nonn

Comments

Indexing starts from zero, with a(0) = 0.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to primorial base

Crossrefs

Cf. A002110, A030308, A143293, A276085, A276156, A283477, A283984.

Programs

PARI

A143293(n) = { if(n==0, return(1)); my(P=1, s=1); forprime(p=2, prime(n), s+=P*=p); s; }; \\ This function from Charles R Greathouse IV, Feb 05 2014
A030308(n,k) = bittest(n,k);
A283985(n) = sum(i=0,(#binary(n)-1),A030308(n,i)*A143293(i));

Python

from sympy import primorial, primepi, prime, primerange, factorint
from operator import mul
from functools import reduce
def a002110(n): return 1 if n<1 else primorial(n)
def a276085(n):
    f=factorint(n)
    return sum([f[i]*a002110(primepi(i) - 1) for i in f])
def P(n): return reduce(mul, [i for i in primerange(2, n + 1)])
def a108951(n):
    f = factorint(n)
    return 1 if n==1 else reduce(mul, [P(i)**f[i] for i in f])
def a019565(n): return reduce(mul, (prime(i+1) for i, v in enumerate(bin(n)[:1:-1]) if v == '1')) if n > 0 else 1 # after Chai Wah Wu
def a(n): return a276085(a108951(a019565(n)))
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 22 2017

Scheme

(define (A283985 n) (A276085 (A283477 n)))

Formula

a(n) = Sum_{k>=0} A030308(n,k)*A143293(k).

a(n) = A276085(A283477(n)).

Other identities. For all n >= 0:

a(2^n) = A143293(n).