OFFSET
1,2
COMMENTS
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
EXAMPLE
Divisors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462.
Divisors of 858 are 1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858.
If one takes the smallest prime-signature representative (A046523) of each these, one gets in both cases [1, 2, 2, 6, 2, 2, 6, 6, 6, 6, 30, 30, 6, 30, 30, 210]. E.g. 462 = 2*3*7*11 and 858 = 2*3*11*13, which both have the same prime signature as 210 = 2*3*5*7. And similarly for all the other divisors, from which follows that a(462) = a(858).
On the other hand, for 12 = 2*2*3 the divisors are 1, 2, 3, 2*2, 2*3, 2*2*3, and for 18 = 2*3*3 the divisors are 1, 2, 3, 2*3, 3*3, 2*3*3, and because the prime signatures differ both in the fourth and in the fifth places, a(18) != a(12).
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; };
write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
v101296 = rgs_transform(vector(up_to, n, A046523(n)));
A101296(n) = v101296[n];
write_to_bfile(1, rgs_transform(vector(up_to, n, A297174(n))), "b300250.txt");
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 07 2018
STATUS
approved