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 A175261 Each term is the smallest positive integer both coprime to all earlier terms of the sequence and with a different number of divisors than all earlier terms. (a(1)=1.) 0
 1, 2, 9, 35, 1573, 7429, 707281, 1315609, 3397301, 12780049, 1855052713 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..11. PROG (PARI) isok(v, vd, nb, k) = {if (vecsearch(vd, numdiv(k)), return (0)); for (j=1, nb, if (gcd(k, v[j]) != 1, return (0)); ); 1; } findk(v, nb) = {my(k = 1); my(vd = vecsort(vector(nb, j, numdiv(v[j])), , 8)); while (!isok(v, vd, nb, k), k++); k; } lista(nn) = {va = vector(nn); print1(va[1] = 1, ", "); for (n=2, nn, k = findk(va, n-1); print1(va[n] = k, ", "); ); } \\ Michel Marcus, Feb 25 2016 (Python) from math import gcd from sympy import divisor_count from itertools import count, islice def agen(): # generator of terms alst, d = [1], {1} while True: yield alst[-1] d.add(divisor_count(alst[-1])) k = alst[-1] + 1 while any(gcd(ai, k)!=1 for ai in alst) or divisor_count(k) in d: k += 1 alst.append(k) print(list(islice(agen(), 8))) # Michael S. Branicky, Feb 21 2023 CROSSREFS Cf. A175231. Sequence in context: A357202 A306791 A175231 * A086556 A319012 A192694 Adjacent sequences: A175258 A175259 A175260 * A175262 A175263 A175264 KEYWORD more,nonn AUTHOR Leroy Quet, Mar 16 2010 EXTENSIONS a(6)-a(10) from Michel Marcus, Feb 25 2016 a(11) from Michael S. Branicky, Feb 22 2023 STATUS approved

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