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A329618 a(n) = gcd(A001222(n), A324888(n)), where A324888(n) is the minimal number of primorials (A002110) that add to A108951(n). 5
1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 4, 1, 1, 1, 1, 2, 2, 1, 4, 2, 2, 1, 1, 1, 3, 1, 1, 2, 2, 2, 4, 1, 2, 2, 2, 1, 1, 1, 1, 3, 2, 1, 1, 2, 3, 2, 1, 1, 4, 2, 4, 2, 2, 1, 2, 1, 2, 3, 2, 2, 3, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 4, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 1, 2, 2, 2, 2, 1, 1, 3, 4, 1, 3, 1, 4, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

FORMULA

a(n) = gcd(A001222(n), A324888(n)) = gcd(A001222(n), A001222(A324886(n))).

MATHEMATICA

With[{b = Reverse@ Prime@ Range@ 120}, Array[GCD[PrimeOmega@ #1, Total@ IntegerDigits[#2, MixedRadix[b]]] & @@ {#, Apply[Times, Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]]} &, 105] ] (* Michael De Vlieger, Nov 18 2019 *)

PROG

(PARI)

A034386(n) = prod(i=1, primepi(n), prime(i));

A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951

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

A324886(n) = A276086(A108951(n));

A329618(n) = gcd(bigomega(n), bigomega(A324886(n)));

CROSSREFS

Cf. A001222, A034386, A108951, A276086, A324886, A324888, A329619, A329620, A329621.

Sequence in context: A190611 A000377 A192013 * A026517 A072047 A327521

Adjacent sequences:  A329615 A329616 A329617 * A329619 A329620 A329621

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 18 2019

STATUS

approved

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Last modified May 15 17:11 EDT 2021. Contains 343920 sequences. (Running on oeis4.)