A322588 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A322588

Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 for odd primes, and f(n) = A291750(n) for any other number.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

For all i, j: a(i) = a(j) => A322318(i) = A322318(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; };

A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };

A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));

Aux322588(n) = if((n>2)&&isprime(n), 0, (1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n)));

v322588 = rgs_transform(vector(up_to, n, Aux322588(n)));

A322588(n) = v322588[n];

CROSSREFS

Cf. A291750, A291751, A322587, A322589, A322591, A322592.

Sequence in context: A326203 A355835 A305896 * A323401 A326199 A329608

Adjacent sequences: A322585 A322586 A322587 * A322589 A322590 A322591

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 18 2018

STATUS

approved