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A277333 Left inverse of A260443, giving 0 as a result when n is outside of the range of A260443. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A291937 A243488 A154849 * A248663 A093443 A099092

Adjacent sequences:  A277330 A277331 A277332 * A277334 A277335 A277336

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 10 2016

STATUS

approved

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Last modified June 18 06:55 EDT 2019. Contains 324203 sequences. (Running on oeis4.)