A326199 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003557(n), A046523(n), A048250(n)] for all other numbers, except f(n) = 0 for odd primes.

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, 32, 3, 33, 34, 35, 32, 36, 3, 37, 32, 38, 39, 40, 3, 41, 3, 42, 43, 44, 45, 46, 3, 47, 42, 46, 3, 48, 3, 49, 50, 51, 42, 52, 3, 53, 54, 55, 3, 56, 57, 58, 59, 60, 3, 61, 62, 63, 64, 65, 59, 66, 3, 67, 68, 69, 3, 70, 3

Offset

1,2

Comments

For all i, j:

A295300(i) = A295300(j) => a(i) = a(j),

A305801(i) = A305801(j) => a(i) = a(j),

a(i) = a(j) => A294877(i) = A294877(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) = n/factorback(factor(n)[, 1]); \\ From A003557
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));
A291750(n) = (1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n));
Aux326199(n) = if((n>2)&&isprime(n), 0, (1/2)*(2 + ((A046523(n) + A291750(n))^2) - A046523(n) - 3*A291750(n)));
v326199 = rgs_transform(vector(up_to, n, Aux326199(n)));
A326199(n) = v326199[n];

Crossrefs

Cf. A003557, A046523, A048250, A294877, A295300, A305801.

Differs from A323401 for the first time at n = 382 where a(382) = 253, while A323401(382) = 140.

Sequence in context: A305896 A322588 A323401 * A329608 A322824 A322314

Adjacent sequences: A326196 A326197 A326198 * A326200 A326201 A326202

Keyword

nonn

Author

Antti Karttunen, Jul 13 2019

Status

approved