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A278525 Filtering sequence (related to prime factorization): a(n) = A046523(A241916(n)). 2
1, 2, 2, 4, 2, 4, 2, 8, 6, 4, 2, 8, 2, 4, 6, 16, 2, 12, 2, 8, 6, 4, 2, 16, 6, 4, 12, 8, 2, 12, 2, 32, 6, 4, 6, 24, 2, 4, 6, 16, 2, 12, 2, 8, 12, 4, 2, 32, 6, 12, 6, 8, 2, 36, 6, 16, 6, 4, 2, 24, 2, 4, 12, 64, 6, 12, 2, 8, 6, 12, 2, 48, 2, 4, 30, 8, 6, 12, 2, 32, 24, 4, 2, 24, 6, 4, 6, 16, 2, 36, 6, 8, 6, 4, 6, 64, 2, 12, 12, 24, 2, 12, 2, 16, 30, 4, 2, 72, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = A046523(A241916(n)).

Other identities. For all n:

a(2^n) = 2^n.

a(A000040(n)) = 2.

PROG

(PARI)

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523

A209229(n) = (n && !bitand(n, n-1));

A241916(n) = if(1==A209229(n), n, my(f = factor(2*n), nbf = #f~, igp = primepi(f[nbf, 1]), g = f); for(i=1, nbf, g[i, 1] = prime(1+igp-primepi(f[i, 1]))); factorback(g)/2);

A278525(n) = A046523(A241916(n)); \\ Antti Karttunen, Jul 02 2018

(Scheme) (define (A278525 n) (A046523 (A241916 n)))

CROSSREFS

Cf. A000040, A046523, A241916, A278220, A278221.

Sequence in context: A061142 A318312 A318474 * A318476 A226083 A182730

Adjacent sequences:  A278522 A278523 A278524 * A278526 A278527 A278528

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 30 2016

STATUS

approved

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Last modified June 19 00:55 EDT 2019. Contains 324217 sequences. (Running on oeis4.)