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

Author

Antti Karttunen, Oct 02 2017

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

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))))))

Formula

For all n >= 0:

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

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