A324541 - OEIS

A324541

Numbers that occur in range of A324580.

0, 2, 6, 18, 30, 36, 70, 90, 120, 210, 270, 300, 434, 450, 650, 672, 990, 1050, 1260, 1386, 2142, 2250, 2310, 2590, 2940, 3600, 3990, 4410, 4642, 4750, 5978, 6996, 7350, 7500, 7650, 8190, 9114, 11880, 12600, 14058, 15000, 15050, 15750, 16170, 18480, 18522, 21186, 23100, 23870, 24750, 25830, 28224, 30030, 30870, 31250, 32830, 35970, 37114, 42000

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

OFFSET

0,2

COMMENTS

Indexing begins from 0 because the term a(0) = 0 is a special case.

Sequence A324580 sorted into ascending order, with duplicate occurrences removed. The first such duplicate is 2250 = A324580(15) = 150*15 = A324580(18) = 125*18. The next is 5402250 = A324580(105) = A276086(105)*105 = A324580(125) = A276086(125)*125.

Terms after zero are the positions of nonzero terms in A324539.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..702

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

PROG

(PARI)

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; };

A324539(n) = sumdiv(n, d, (d==A276086(n/d)));

for(n=1, oo, if(A324539(n)>0, print1(n, ", "))); \\ Print terms after zero.

(PARI)

\\ This program is better for computing many terms:

search_limit = 9699690;

A324580(n) = n*A276086(n);

A324541list(lim) = { my(s=Set([]), k); for(n=1, lim, k=A324580(n); if(k<=lim, s = setunion([k], s))); Vec(s); };

v324541 = A324541list(search_limit);

A324541(n) = if(!n, n, v324541[n]);

CROSSREFS

Cf. A324540 (complement).

Cf. A002110 (a subsequence), A276086, A324539, A324579, A324580.