A329618 - OEIS

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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).

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

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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: A000377 A192013 A373989 * A374033 A026517 A072047

Adjacent sequences: A329615 A329616 A329617 * A329619 A329620 A329621

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 18 2019

STATUS

approved