A291751 Lexicographically earliest such sequence a that a(i) = a(j) => A003557(i) = A003557(j) and A048250(i) = A048250(j), for all i, j.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 6, 11, 12, 13, 13, 14, 10, 15, 16, 17, 18, 19, 13, 20, 21, 22, 23, 24, 25, 26, 18, 27, 28, 29, 28, 30, 31, 32, 33, 34, 22, 35, 36, 37, 38, 26, 28, 39, 40, 41, 26, 42, 29, 43, 26, 44, 45, 46, 32, 47, 48, 35, 49, 50, 51, 52, 53, 54, 35, 52, 26, 55, 56, 57, 58, 59, 35, 60, 45, 61, 62, 63, 51, 64, 65, 66, 67, 68, 46, 69, 70, 47, 71

Offset: 1

Author

Antti Karttunen, Sep 06 2017

Keywords

• nonn

Comments

Restricted growth sequence transform of A291750, which means that this is the lexicographically least sequence a, such that for all i, j: a(i) = a(j) <=> A291750(i) = A291750(j) <=> A003557(i) = A003557(j) and A048250(i) = A048250(j). That this is equal to the definition given in the title follows because any such lexicographically least sequence satisfying relation <=> is also the least sequence satisfying relation => with the same parameters.

Sigma (A000203) and psi (A001615) are functions of this sequence. See comments in A291750 for the reason. For example, to find the value of A001615(n) when we know just a(n), but without knowing n, let m be the least i for which a(i) = a(n); then A001615(n) = A003991(A291750(m)) = A003557(m) * A048250(m).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A001615, A003557, A048250, A291750, A291752, A294877, A295300, A295886, A295887, A295888, A319698, A322021.

Differs from A286603 for the first time at n = 25, where a(25) = 21, while A286603(25) = 14.

Programs

PARI

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; };
A003557(n) = n/factorback(factor(n)[, 1]); \\ From A003557
A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));
A291750(n) = (1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n));
v291751 = rgs_transform(vector(65537,n,A291750(n)));
A291751(n) = v291751[n];

Extensions

Name changed and comments added by Antti Karttunen, Nov 24 2018