A324582 - OEIS

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A324582

a(n) = A002182(n) * A324581(n) = A002182(n) * A276086(A002182(n)).

5

2, 6, 36, 30, 300, 15000, 1260, 42000, 2940, 288120, 21176820, 18480, 66555720, 328703760, 12298440, 2232166860, 360122920080, 360360, 103062960, 22107004920, 4215068938080, 129290917072196880, 3525159950945805332160, 90107494796113466546674800, 645822919595173320, 72532204477502449680, 1648012277067163992784800

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Note that gcd(A002182(n), A324581(n)) = A324198(A002182(n)) = 1 for all n because each term of A002182 is a product of primorial numbers (A002110).

See also comments in A324382.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..512

Michael De Vlieger, Small chart of first terms.

Michael De Vlieger, 2400 x 3600 chart of first terms.

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

FORMULA

a(n) = A002182(n) * A324581(n) = A002182(n) * A276086(A002182(n)).

a(n) = A324580(A002182(n)).

MATHEMATICA

Block[{b = MixedRadix[Reverse@ Prime@ Range@ 20], s = DivisorSigma[0, Range[10^5]], t}, t = Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]; Array[#1 (Times @@ Power @@@ Transpose@ {Prime@ Range@ Length@ #2, Reverse@ #2}) & @@ {#, IntegerDigits[#, b]} &@ t[[#]] &, Length@ t]] (* Michael De Vlieger, Mar 18 2019 *)

PROG

(PARI)

\\ A002182 assumed to be precomputed

A276086(n) = { my(i=0, m=1, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m*=(prime(i)^((n%nextpr)/pr)); n-=(n%nextpr)); pr=nextpr); m; };

A324582(n) = A002182(n)*A276086(A002182(n));

CROSSREFS

Subsequence of A324577.

Cf. A002110, A002182, A276086, A324198, A324382, A324580, A324581.

Sequence in context: A193190 A247209 A324577 * A275600 A226368 A058083

Adjacent sequences: A324579 A324580 A324581 * A324583 A324584 A324585

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 09 2019

STATUS

approved