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A327858 Greatest common divisor of the arithmetic derivative and the primorial base exp-function: a(n) = gcd(A003415(n), A276086(n)). 28
1, 2, 1, 1, 1, 1, 5, 1, 3, 6, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 3, 10, 1, 1, 1, 10, 15, 3, 1, 1, 1, 1, 1, 14, 1, 6, 5, 1, 21, 2, 1, 1, 1, 1, 3, 3, 25, 1, 7, 14, 15, 10, 7, 1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 3, 3, 18, 1, 1, 3, 2, 1, 1, 1, 1, 3, 5, 5, 18, 1, 1, 1, 6, 1, 1, 1, 2, 15, 2, 35, 1, 1, 2, 3, 2, 49, 6, 1, 1, 7, 15, 35, 1, 7, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequence contains only terms of A048103.

Proof that A046337 gives the positions of even terms: see Charlie Neder's Feb 25 2019 comment in A235992 and recall that A276086 is never a multiple of 4, as it is a permutation of A048103, and furthermore it toggles the parity. See also comment in A327860. - Antti Karttunen, May 01 2022

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to primorial base

FORMULA

a(n) = gcd(A003415(n), A276086(n)).

a(p) = 1 for all primes p.

a(n) = A276086(A351234(n)). - Antti Karttunen, May 01 2022

MATHEMATICA

Block[{b = MixedRadix[Reverse@ Prime@ Range@ 12], f, g}, f[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]]; g[n_] := Times @@ Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ #, Reverse@ #} &@ IntegerDigits[n, b]; Array[GCD[f@ #, g@ #] &, 105]] (* Michael De Vlieger, Sep 30 2019 *)

PROG

(PARI)

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

A327858(n) = gcd(A003415(n), A276086(n));

CROSSREFS

Cf. A003415, A048103, A235992, A276086, A327859, A351234.

Cf. A046337 (positions of even terms).

Cf. also A085731, A324198, A328572 [= gcd(A276086(n), A327860(n))], A345000.

Sequence in context: A181937 A233836 A214719 * A307372 A259681 A146314

Adjacent sequences:  A327855 A327856 A327857 * A327859 A327860 A327861

KEYWORD

nonn,base,easy

AUTHOR

Antti Karttunen, Sep 30 2019

EXTENSIONS

Verbal description added to the definition by Antti Karttunen, May 01 2022

STATUS

approved

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Last modified October 5 17:43 EDT 2022. Contains 357261 sequences. (Running on oeis4.)