A277333 Left inverse of A260443, giving 0 as a result when n is outside of the range of A260443.

0, 1, 2, 0, 4, 3, 8, 0, 0, 0, 16, 0, 32, 0, 6, 0, 64, 5, 128, 0, 0, 0, 256, 0, 0, 0, 0, 0, 512, 7, 1024, 0, 0, 0, 12, 0, 2048, 0, 0, 0, 4096, 0, 8192, 0, 0, 0, 16384, 0, 0, 0, 0, 0, 32768, 0, 0, 0, 0, 0, 65536, 0, 131072, 0, 0, 0, 0, 0, 262144, 0, 0, 0, 524288, 0, 1048576, 0, 10, 0, 24, 0, 2097152, 0, 0, 0, 4194304, 0, 0, 0, 0, 0, 8388608, 9

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..5000

Formula

If A260443(A048675(n)) = n, then a(n) = A048675(n), otherwise a(n) = 0.

Other identities. For all n >= 0:

a(A260443(n)) = n.

a(2n+1) = 2*a(A064989(2n+1)).

If a(2n) > 0 [by necessity an odd number in that case], then A005811((a(2n)-1)/2) = A007949(2n). [See comment in A277324.]

Example

a(1) = 0 because A260443(0) = 1. For n > 1, a(n) = 0 only if n does not occur in the range of A260443.
a(6) = 3 because A260443(3) = 6.

Prog

(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ Michel Marcus, Oct 10 2016
A260443(n) = if(n<2, n+1, if(!(n%2), A003961(A260443(n/2)), A260443((n-1)/2) * A260443((n+1)/2)));
A277333(n) = { my(k=A048675(n)); if(A260443(k) == n, k, 0); } ;
for(n=1, 5000, write("b277333.txt", n, " ", A277333(n)));
(Scheme) (define (A277333 n) (let ((k (A048675 n))) (if (= (A260443 k) n) k 0)))

Crossrefs

Cf. A005811, A007949, A048675, A064989, A260443.

Cf. A277316, A260442 (from 2 onward, the positions of nonzeros), A277317 (positions of primes).

Sequence in context: A154849 A339261 A345232 * A248663 A335426 A348405

Adjacent sequences: A277330 A277331 A277332 * A277334 A277335 A277336

Keyword

nonn

Author

Antti Karttunen, Oct 10 2016

Status

approved