A332230 - OEIS

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A332230

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(2^k) = 0 for k >= 2.

1, 2, 3, 4, 5, 6, 7, 4, 8, 9, 10, 11, 12, 13, 13, 4, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 4, 29, 30, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 41, 46, 47, 48, 41, 49, 50, 51, 52, 53, 54, 55, 56, 4, 57, 58, 59, 60, 55, 58, 61, 62, 63, 64, 65, 66, 55, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 76

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

OFFSET

1,2

COMMENTS

For all i, j:

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

a(i) = a(j) => A048250(i) = A048250(j),

a(i) = a(j) => A332455(i) = A332455(j),

a(i) = a(j) => A332459(i) = A332459(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)));

A209229(n) = (n && !bitand(n, n-1));

A291750(n) = (1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n));

Aux332230(n) = if((n>2)&&A209229(n), 0, (1/2)*(2 + ((A046523(n) + A291750(n))^2) - A046523(n) - 3*A291750(n)));

v332230 = rgs_transform(vector(up_to, n, Aux332230(n)));

A332230(n) = v332230[n];

CROSSREFS

Cf. A003557, A046523, A048250, A295300, A332455, A332459.

Cf. also A326199.

Sequence in context: A366392 A272573 A328477 * A319999 A083501 A007922

Adjacent sequences: A332227 A332228 A332229 * A332231 A332232 A332233

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 22 2020

STATUS

approved