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A292265 A multiplicative encoding (compressed) for the exponents of 2 obtained when using Shevelev's algorithm for computing A002326. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A124442 A220271 A088611 * A259416 A137765 A287509

Adjacent sequences:  A292262 A292263 A292264 * A292266 A292267 A292268

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 02 2017

STATUS

approved

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Last modified May 21 03:31 EDT 2022. Contains 353887 sequences. (Running on oeis4.)