A296090 Filter combining the sum of divisors (A000203) and prime-signature (A101296) of n; restricted growth sequence transform of A286360.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 44, 49, 50, 51, 44, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 57, 61, 64, 65, 66, 67, 68, 69, 57, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 79

Offset

1,2

Comments

For all i, j:

a(i) = a(j) => A286034(i) = A286034(j).

a(i) = a(j) => A295880(i) = A295880(j).

Links

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

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])); }
A000203(n) = sigma(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
A286360(n) = (1/2)*(2 + ((A046523(n)+A000203(n))^2) - A046523(n) - 3*A000203(n));
write_to_bfile(1, rgs_transform(vector(up_to, n, A286360(n))), "b296090.txt");

Crossrefs

Cf. A000203, A101296, A046523, A286034, A286360, A295300, A295888, A296089.

Differs from related A295880 for the first time at n=135, where a(135) = 123, while A295880(135) = 104.

Sequence in context: A322021 A295888 A295880 * A323372 A295300 A139179

Adjacent sequences: A296087 A296088 A296089 * A296091 A296092 A296093

Keyword

nonn

Author

Antti Karttunen, Dec 07 2017

Status

approved