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

Offset: 0

Author

Antti Karttunen, Oct 02 2017

Keywords

• nonn

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

Crossrefs

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

Programs

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))))))

Formula

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