A292265 - OEIS

A292265

A multiplicative encoding (compressed) for the exponents of 2 obtained when using Shevelev's algorithm for computing A002326.

2, 3, 12, 6, 20, 180, 720, 5, 80, 25920, 20, 360, 43200, 25920, 6220800, 10, 240, 540, 671846400, 540, 57600, 2160, 540, 194400, 155520, 45, 5804752896000, 77760, 14400, 87071293440000, 348285173760000, 15, 960, 12538266255360000, 311040, 139968000, 120, 77760, 18662400, 1679616000, 23219011584000, 108330620446310400000, 60, 4665600, 360, 540, 180

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OFFSET

0,1

COMMENTS

a(n) = A019565(v(1)) * A019565(v(2)) * ... * A019565(v(k)), where v(1) .. v(k) are 2-adic valuations (not all necessarily distinct) of the iterated values obtained when running Shevelev's algorithm for computing A002623. (See A179680 and A292239.)

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..1023

FORMULA

For all n >= 0, A048675(a(n)) = A002326(n).

PROG

(PARI)

A000265(n) = (n >> valuation(n, 2));

A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler

A292265(n) = { my(x = n+n+1, z = A019565(valuation(1+x, 2)), m = A000265(1+x)); while(m!=1, z *= A019565(valuation(x+m, 2)); m = A000265(x+m)); z; };

(Scheme) (define (A292265 n) (let ((x (+ n n 1))) (let loop ((z (A019565 (A007814 (+ 1 x)))) (k 1)) (let ((m (A000265 (+ x k)))) (if (= 1 m) z (loop (* z (A019565 (A007814 (+ x m)))) m))))))

CROSSREFS

Cf. A000265, A002326, A007814, A019565, A179680, A292239 (a variant), A292266 (rgs-version of this filter).

Sequence in context: A220271 A088611 A361323 * A259416 A137765 A356946

Adjacent sequences: A292262 A292263 A292264 * A292266 A292267 A292268

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 02 2017

STATUS

approved