A292239 A multiplicative encoding for the exponents of 2 obtained when using Shevelev's algorithm for computing A002326.

2, 3, 10, 5, 28, 252, 840, 7, 88, 23760, 22, 330, 66528, 23760, 6652800, 11, 208, 468, 471744000, 390, 58240, 1872, 468, 163800, 93600, 39, 3736212480000, 39000, 17472, 94152554496000, 313841848320000, 13, 544, 7387354275840000, 146880, 84823200, 68, 36720, 12337920, 1079568000

Offset

0,1

Comments

a(n) = prime(v(1)) * prime(v(2)) * ... * prime(v(k)), where prime(n) is the n-th prime (= A000040(n)) and v(1) .. v(k) are 2-adic valuations (not all necessarily distinct) of the iterated values obtained when running Shevelev's algorithm for computing A002326. See comments in A179680 and compare to A292265.

Links

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

Formula

For all n >= 0:

A001222(a(n)) = A179382(1+n).

A056239(a(n)) = A002326(n).

Mathematica

a265[n_] := n/2^IntegerExponent[n, 2];
a[n_] := Module[{x, z, m}, x = 2 n + 1; z = Prime[IntegerExponent[1 + x, 2]]; m = a265[1 + x]; While[m != 1, z *= Prime[IntegerExponent[x + m, 2]]; m = a265[x + m]]; z];
Table[a[n], {n, 0, 39}] (* Jean-François Alcover, Oct 03 2017, translated from PARI *)

Prog

(PARI)
A000265(n) = (n >> valuation(n, 2));
A292239(n) = { my(x = n+n+1, z = prime(valuation(1+x, 2)), m = A000265(1+x)); while(m!=1, z *= prime(valuation(x+m, 2)); m = A000265(x+m)); z; };
(Scheme) (define (A292239 n) (let ((x (+ n n 1))) (let loop ((z (A000040 (A007814 (+ 1 x)))) (k 1)) (let ((m (A000265 (+ x k)))) (if (= 1 m) z (loop (* z (A000040 (A007814 (+ x m)))) m))))))

Crossrefs

Cf. A000040, A000265, A002326, A007814, A179382, A179680, A292265 (a variant).

Sequence in context: A064946 A078730 A334628 * A163767 A343936 A336091

Adjacent sequences: A292236 A292237 A292238 * A292240 A292241 A292242

Keyword

nonn

Author

Antti Karttunen, Oct 02 2017

Status

approved