login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A366384
Lexicographically earliest infinite sequence such that a(i) = a(j) => A355828(i) = A355828(j) for all i, j >= 1, where A355828 is Dirichlet inverse of A342671, the greatest common divisor of sigma(n) and A003961(n).
1
1, 2, 3, 4, 3, 5, 3, 6, 7, 5, 3, 8, 3, 5, 1, 9, 3, 7, 3, 10, 1, 5, 3, 11, 7, 5, 12, 8, 3, 2, 3, 13, 1, 5, 1, 7, 3, 5, 1, 14, 3, 2, 3, 15, 7, 5, 3, 7, 7, 7, 1, 8, 3, 11, 1, 16, 2, 5, 3, 17, 3, 5, 7, 18, 19, 2, 3, 20, 1, 2, 3, 11, 3, 5, 7, 8, 1, 2, 3, 21, 4, 5, 3, 4, 1, 5, 2, 22, 3, 7, 1, 15, 1, 5, 1, 23, 3, 7, 24
OFFSET
1,2
LINKS
PROG
(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; };
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1])*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A342671(n) = gcd(sigma(n), A003961(n));
v366384 = rgs_transform(DirInverseCorrect(vector(up_to, n, A342671(n))));
A366384(n) = v366384[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 12 2023
STATUS
approved