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 A279686 Numbers that are the least integer of a prime tower factorization equivalence class (see Comments for details). 4
 1, 2, 4, 6, 8, 12, 16, 18, 30, 36, 40, 48, 60, 64, 72, 81, 90, 108, 144, 162, 180, 192, 200, 210, 225, 240, 256, 280, 320, 324, 360, 405, 420, 432, 450, 500, 512, 540, 576, 600, 630, 648, 720, 768, 810, 900, 960, 1260, 1280, 1296, 1350, 1400, 1536, 1575, 1600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The prime tower factorization of a number is defined in A182318. We say that two numbers, say n and m, belong to the same prime tower factorization equivalence class iff there is a permutation of the prime numbers, say f, such that replacing each prime p by f(p) in the prime tower factorization of n leads to m. The notion of prime tower factorization equivalence class can be seen as a generalization of the notion of prime signature; thereby, this sequence can be seen as an equivalent of A025487. This sequence contains all primorial numbers (A002110). This sequence contains A260548. This sequence contains the terms > 0 in A014221. If n appears in the sequence, then 2^n appears in the sequence. If n appears in the sequence and k>=0, then A002110(k)^n appears in the sequence. With the exception of term 1, this sequence contains no term from A182318. Odd numbers appearing in this sequence: 1, 81, 225, 405, 1575, 2025, 2835, 6125, 10125, 11025, 14175, 15625, 16875, 17325, 31185, 33075, 50625, 67375, 70875, 99225, ... Here are some prime tower factorization equivalence classes: - Class 1: the number one (the only finite equivalence class), - Class p: the prime numbers (A000040), - Class p*q: the squarefree semiprimes (A006881), - Class p^p: the numbers of the form p^p with p prime (A051674), - Class p^q: the numbers of the form p^q with p and q distinct primes, - Class p*q*r: the sphenic numbers (A007304), - Class p*q*r*s: the products of four distinct primes (A046386), - Class p*q*r*s*t: the products of five distinct primes (A046387), - Class p*q*r*s*t*u: the products of six distinct primes (A067885). LINKS Rémy Sigrist, Table of n, a(n) for n = 1..1000 Rémy Sigrist, PARI program for A279686 Rémy Sigrist, Prime tower factorization of the first terms EXAMPLE 2 is the least number of the form p with p prime, hence 2 appears in the sequence. 6 is the least number of the form p*q with p and q distinct primes, hence 6 appears in the sequence. 72 is the least number of the form p^q*q^p with p and q distinct primes, hence 72 appears in the sequence. 36000 is the least number of the form p^q*q^r*r^p with p, q and r distinct primes, hence 36000 appears in the sequence. CROSSREFS Cf. A000040, A002110, A006881, A007304, A014221, A025487, A046386, A046387, A051674, A067885, A182318, A260548, A279690. Sequence in context: A322492 A332276 A317246 * A219653 A050622 A082662 Adjacent sequences:  A279683 A279684 A279685 * A279687 A279688 A279689 KEYWORD nonn AUTHOR Rémy Sigrist, Dec 16 2016 STATUS approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)