A112642 Primorial number quotients arising in A007684: a(n) = A002110(A007684(n))/A002110(n-1).

6, 15015, 33426748355, 1357656019974967471687377449, 7105630242567996762185122555313528897845637444413640621, 1924344668948998025181489521338230544342953524990122861050411878226909135705454891961917517

Offset

1,1

Comments

These numbers are (perhaps the smallest) squarefree solutions to Puzzle 329 of Rivera; a(n) is abundant, not divisible by the first n-1 prime numbers, i.e., the least prime divisor of a(n) is the n-th prime number.

Duplicate of A007702.

Links

Table of n, a(n) for n=1..6.

Carlos Rivera, Puzzle 329. Odd abundant numbers not divided by 2 or 3, The Prime Puzzles and Problems Connection.

Formula

a(n) = A002110(A007684(n))/A002110(n-1).

Example

The corresponding sigma(a(n))/a(n) abundance ratios are as follows: 2, 2.14825, 2.00097, 2.01433, 2.00587, 2.00101, ...;
the terms have 2,3,5,7,11,... as least prime divisors.

Crossrefs

Cf. A007702, A002110, A007684, A064001, A110585, A112640.

Sequence in context: A062782 A036773 A007702 * A130434 A121571 A123659

Adjacent sequences: A112639 A112640 A112641 * A112643 A112644 A112645

Keyword

nonn

Author

Labos Elemer, Sep 19 2005

Extensions

Term a(2) and name corrected by Andrey Zabolotskiy, Jul 16 2022

Status

approved