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

%I A292239 #16 Oct 04 2017 14:04:15
%S A292239 2,3,10,5,28,252,840,7,88,23760,22,330,66528,23760,6652800,11,208,468,
%T A292239 471744000,390,58240,1872,468,163800,93600,39,3736212480000,39000,
%U A292239 17472,94152554496000,313841848320000,13,544,7387354275840000,146880,84823200,68,36720,12337920,1079568000
%N A292239 A multiplicative encoding for the exponents of 2 obtained when using Shevelev's algorithm for computing A002326.
%C A292239 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.
%H A292239 Antti Karttunen, <a href="/A292239/b292239.txt">Table of n, a(n) for n = 0..1023</a>
%F A292239 For all n >= 0:
%F A292239 A001222(a(n)) = A179382(1+n).
%F A292239 A056239(a(n)) = A002326(n).
%t A292239 a265[n_] := n/2^IntegerExponent[n, 2];
%t A292239 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];
%t A292239 Table[a[n], {n, 0, 39}] (* _Jean-François Alcover_, Oct 03 2017, translated from PARI *)
%o A292239 (PARI)
%o A292239 A000265(n) = (n >> valuation(n, 2));
%o A292239 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; };
%o A292239 (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))))))
%Y A292239 Cf. A000040, A000265, A002326, A007814, A179382, A179680, A292265 (a variant).
%K A292239 nonn
%O A292239 0,1
%A A292239 _Antti Karttunen_, Oct 02 2017