A300235 Restricted growth sequence transform of A291765, filter combining A001065(n) and A046523(n), the sum of proper divisors and the prime signature of n.

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

Offset

1,2

Links

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

Example

a(51) = a(91) (= 33) because both are nonsquare semiprimes (3*17 and 7*13), and the sum of their proper divisors (A001065) are equal 1+3+17 = 1+7+13 = 21.

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])); }
A001065(n) = (sigma(n)-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
A291765(n) = (1/2)*(2 + ((A001065(n)+A046523(n))^2) - A001065(n) - 3*A046523(n));
write_to_bfile(1, rgs_transform(vector(up_to, n, A291765(n))), "b300235.txt");

Crossrefs

Cf. A001065, A046523, A291765.

Cf. also A295885, A300223, A300226, A300229, A300230, A300231, A300232, A300233.

Sequence in context: A319348 A353560 A300249 * A351260 A305895 A327931

Adjacent sequences: A300232 A300233 A300234 * A300236 A300237 A300238

Keyword

nonn

Author

Antti Karttunen, Mar 01 2018

Status

approved