A354233 Least number with n runs in ordered prime signature.

1, 2, 12, 90, 2100, 48510, 3303300, 139369230, 18138420300, 1157182716690, 278261505822300, 30168910606824990, 9894144362523521100, 1693350783450479863710, 715178436956287675671300, 147157263134197051595990130, 83730945863531292204568790100

Offset: 0

Author

Gus Wiseman, May 20 2022

Keywords

• nonn

Comments

A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.

Examples

			The prime indices of 90 are {1,2,2,3}, with multiplicities {1,2,1}, with runs {{1},{2},{1}}, and this is the first case of 3 runs, so a(3) = 90.
		

Links

• Mathematics Stack Exchange, What is a sequence run? (answered 2011-12-01)

Crossrefs

Positions of first appearances in A353745.

A001222 counts prime factors with multiplicity, distinct A001221.

A005361 gives product of signature, firsts A353500 (sorted A085629).

A056239 adds up prime indices, row sums of A112798 and A296150.

A124010 gives prime signature, sorted A118914.

A130091 lists numbers with distinct prime exponents, counted by A098859.

A181819 gives prime shadow, with an inverse A181821.

A182850 gives frequency depth of prime indices, counted by A225485.

A323014 gives adjusted frequency depth of prime indices, counted by A325280.

Cf. A005811, A097318, A304678, A325755, A353507, A353742.

Programs

Mathematica

Table[Product[Prime[i]^If[EvenQ[n-i],1,2],{i,n}],{n,0,15}]