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a(1) = 1. a(n) = the smallest integer which is > a(n-1) and is different from and not coprime to A134623(n-1).
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%I #13 Sep 07 2019 20:50:19

%S 1,4,6,10,14,16,18,22,24,26,27,34,38,40,42,46,50,52,58,60,62,64,66,70,

%T 72,74,75,82,86,88,90,94,96,98,99,106,108,110,112,114,118,122,123,125,

%U 134,136,138,142,146,148,154,156,158,160,162,166,168,170,171,178,182

%N a(1) = 1. a(n) = the smallest integer which is > a(n-1) and is different from and not coprime to A134623(n-1).

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a134/A134624.java">Java program</a> (github)

%o (PARI) missing(n, v) = {my(nb = 0, k = 1, s = Set(v), ok = 0); while(!ok, if (! setsearch(s, k), nb++); ok = (nb == n); if (!ok, k++);); k;}

%o nextt(start, cop) = {my(k = max(start+1, cop+1)); while(gcd(k, cop) == 1, k++); k;}

%o list4(nn) = {my(v3 = vector(nn), v4 = vector(nn)); v4[1] = 1; for (n=1, nn, v3[n] = missing(n, v4); if (n+1 > nn, break); v4[n+1] = nextt(v4[n], v3[n]);); v4} \\ _Michel Marcus_, Sep 06 2019

%Y Cf. A134623(n) = the n-th positive integer which is missing from {a(k)}.

%K nonn

%O 1,2

%A _Leroy Quet_, Nov 04 2007

%E Name and one term corrected and extended by _Michel Marcus_, Sep 06 2019