proposed

approved

editing

proposed

Antti Karttunen, <a href="/A322588/b322588.txt">Table of n, a(n) for n = 1..65537</a>

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

allocatedLexicographically 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 Anttiother Karttunennumber.

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

1,2

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

(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];

Cf. A291750, A291751,

allocated

nonn

Antti Karttunen, Dec 18 2018

approved

editing

allocated for Antti Karttunen

allocated

approved