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A292239 A multiplicative encoding for the exponents of 2 obtained when using Shevelev's algorithm for computing A002326. 7
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A175899 A064946 A078730 * A163767 A128531 A123167

Adjacent sequences:  A292236 A292237 A292238 * A292240 A292241 A292242

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 02 2017

STATUS

approved

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Last modified August 15 09:12 EDT 2018. Contains 313756 sequences. (Running on oeis4.)