A295888 Filter combining prime signature of n (A101296) with Dedekind's psi (A001615).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 41, 42, 43, 44, 45, 46, 42, 47, 48, 49, 42, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 56, 60, 63, 64, 65, 66, 67, 67, 56, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 77

Offset

1,2

Links

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

Eric Weisstein's World of Mathematics, Pairing Function

Wikipedia, Pairing Function

Formula

Restricted growth sequence transform of function f(n) = (1/2)*(2 + ((A046523(n) + A001615(n))^2) - A046523(n) - 3*A001615(n)), where values A046523(n) and A001615(n) are packed together to a(n) with the 2-argument form of A000027, also known as Cantor pairing-function.

Prog

(PARI)
allocatemem(2^30);
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])); }
A001615(n) = (n * sumdivmult(n, d, issquarefree(d)/d)); \\ This function from Charles R Greathouse IV, Sep 09 2014
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
Anotsubmitted8(n) = (1/2)*(2 + ((A046523(n)+A001615(n))^2) - A046523(n) - 3*A001615(n));
write_to_bfile(1, rgs_transform(vector(up_to, n, Anotsubmitted8(n))), "b295888.txt");

Crossrefs

Cf. A001615, A046523, A101296, A291750, A295300, A295880, A295887, A296090.

Sequence in context: A124196 A293704 A322021 * A295880 A296090 A323372

Adjacent sequences: A295885 A295886 A295887 * A295889 A295890 A295891

Keyword

nonn

Author

Antti Karttunen, Dec 03 2017

Status

approved