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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. 9
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 (list; graph; refs; listen; history; text; internal format)
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: A344025 A319348 A300249 * A305895 A327931 A300833

Adjacent sequences:  A300232 A300233 A300234 * A300236 A300237 A300238

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 01 2018

STATUS

approved

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Last modified July 25 13:05 EDT 2021. Contains 346290 sequences. (Running on oeis4.)