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A300225
Filter sequence combining A296078(n) and A296091(n), the prime signatures of phi(n)+1 and sigma(n)-1, with a(1) = 1.
4
1, 2, 2, 3, 2, 2, 2, 3, 4, 2, 2, 5, 2, 2, 6, 7, 2, 3, 2, 6, 2, 3, 2, 6, 8, 2, 3, 3, 2, 6, 2, 3, 9, 2, 6, 10, 2, 2, 11, 2, 2, 3, 2, 9, 11, 2, 2, 3, 12, 13, 9, 6, 2, 3, 2, 11, 2, 2, 2, 2, 2, 3, 2, 14, 6, 15, 2, 16, 17, 11, 2, 11, 2, 2, 3, 2, 3, 6, 2, 15, 18, 5, 2, 6, 9, 2, 15, 2, 2, 6, 3, 19, 2, 3, 3, 9, 2, 20, 3, 21, 2, 15, 2, 11, 6
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of P(A296078(n), A296091(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.
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; };
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]); }; \\ This function from Charles R Greathouse IV, Aug 17 2011
A296078(n) = A046523(1+eulerphi(n));
A296091(n) = if(1==n, n, A046523(sigma(n)-1); )
Aux300225(n) = (1/2)*(2 + ((A296078(n)+A296091(n))^2) - A296078(n) - 3*A296091(n));
write_to_bfile(1, rgs_transform(vector(up_to, n, Aux300225(n))), "b300225.txt");
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 01 2018
STATUS
approved