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

Author

Antti Karttunen, Oct 10 2016

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

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

Programs

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)))

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.]