A324257 Conceited Numbers: Composite numbers that are a concatenation of their distinct prime factors with multiplicity in some order allowing overlap.

735, 3792, 13377, 21372, 51375, 67335, 119911, 229912, 290912, 537975, 1341275, 1713192, 2317312, 2333772, 2971137, 3719193, 4773132, 5117695, 7237755, 7747292, 11973192, 13115375, 13731373, 16749933, 19853575, 22940075, 29090912, 29373375

Offset

1,1

Comments

"Conceited Numbers" (they are full of themselves).

The decimal representation of these numbers can be formed typographically from their prime factors. Every distinct prime factor must appear at least once. Generalization of the sequence A083359.

Subsequences:

--No overlap: A324258

--Every prime factor appears in number (not just distinct prime factors): A324259

--No multiplicity: A324260

--Multiplicity only up to the exponent of the distinct prime factor: A083359

Other subsequences are formed by more than one constraint; e.g., A121342 is the intersection of A324258 and A324260, terms with no overlap and no multiplicity.

Links

Giovanni Resta, Table of n, a(n) for n = 1..302 (first 103 terms from Deron Stewart)

Deron Stewart, C# method to evaluate candidate terms given the distinct prime factors.

Example

67335 = 3*5*67^2 formed by 67||3|||3||5 (this term is not in A083359 because two 3's are required in the concatenation).
3719193 = 3*19*71*919 formed by 3||71||9(19)||3 where 19 and 919 overlap.

Crossrefs

Cf. A324258, A324259, A324260, A083359, A083360, A083361, A121342.

Sequence in context: A250053 A227755 A096595 * A083359 A324258 A083360

Adjacent sequences: A324254 A324255 A324256 * A324258 A324259 A324260

Keyword

nonn,base

Author

Deron Stewart, Feb 19 2019

Status

approved