A354903 Lexicographically earliest infinite sequence of distinct positive integers such that the number of divisors of a(n+1) is prime to a(n).
1, 2, 4, 9, 3, 5, 6, 16, 25, 7, 8, 36, 64, 49, 10, 100, 121, 11, 12, 81, 13, 14, 144, 625, 15, 17, 18, 729, 19, 20, 169, 21, 22, 196, 225, 23, 24, 1024, 256, 289, 26, 324, 1296, 2401, 27, 29, 28, 361, 30, 4096, 400, 441, 31, 32, 484, 529, 33, 34, 576, 5184
Offset: 1
Keywords
Examples
a(7)=6 and 16 is the smallest number which has not already occurred whose number of divisors (5) is prime to 6, therefore a(8)=16.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..16384 first 1237 terms from Rémy Sigrist.
- Michael De Vlieger, Mathematica code.
- Rémy Sigrist, C program
Programs
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C
// See Links section.
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PARI
lista(nn) = my(va = vector(nn)); va[1] = 1; for (n=2, nn, my(k=1); while ((gcd(va[n-1], numdiv(k)) != 1) || #select(x->(x==k), va), k++); va[n] = k;); va; \\ Michel Marcus, Jun 11 2022
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Python
from math import gcd from sympy import divisor_count from itertools import count, islice def agen(): # generator of terms aset, k, mink = {1}, 1, 2; yield 1 for n in count(2): an, k = k, mink while k in aset or not gcd(an, divisor_count(k)) == 1: k += 1 aset.add(k); yield k while mink in aset: mink += 1 print(list(islice(agen(), 60))) # Michael S. Branicky, Jun 11 2022
Extensions
a(15) and beyond from Michael S. Branicky, Jun 11 2022
Comments