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

Offset: 0

Author

Antti Karttunen, Mar 10 2019

Keywords

• nonn

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

Crossrefs

Cf. A324540 (complement).

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

Programs

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]);