cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A324181 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A324180(n) for n > 1 and f(1) = -1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 4, 5, 6, 2, 4, 2, 7, 8, 9, 2, 6, 2, 4, 10, 11, 2, 4, 12, 13, 8, 4, 2, 6, 2, 14, 15, 16, 17, 9, 2, 18, 19, 14, 2, 7, 2, 4, 8, 20, 2, 4, 21, 7, 22, 4, 2, 7, 23, 24, 25, 26, 2, 14, 2, 27, 8, 28, 29, 11, 2, 4, 30, 7, 2, 4, 2, 31, 10, 4, 32, 13, 2, 24, 33, 34, 2, 24, 35, 36, 37, 38, 2, 7, 39, 4, 40, 41, 42, 4, 2, 11, 8, 43, 2, 16, 2, 44, 10
Offset: 1

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Author

Antti Karttunen, Feb 19 2019

Keywords

Comments

For all i, j: a(i) = a(j) => A324120(i) = A324120(j).

Crossrefs

Cf. A000040 (positions of 2's), A156552, A297112, A324120, A324180.
Cf. also A300827, A323914, A324203.

Programs

  • PARI
    up_to = 65537;
    rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
    A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
    A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
    A297112(n) = if(1==n, 0, 2^A297167(n));
    A324180(n) = { my(v=0); fordiv(n, d, if(dA297112(d)))); (v); };
    Aux324181(n) = if((1==n),-n,A324180(n));
    v324181 = rgs_transform(vector(up_to, n, Aux324181(n)));
    A324181(n) = v324181[n];