A379001 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j), v_2(i) = v_2(j), v_3(i) = v_3(j) and v_5(i) = v_5(j), for all i, j, where v_2 (A007814), v_3 (A007949) and v_5 (A112765) give the 2-, 3- and 5-adic valuations of n respectively.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 7, 11, 7, 12, 13, 14, 7, 15, 7, 16, 17, 12, 7, 18, 19, 12, 20, 21, 7, 22, 7, 23, 17, 12, 24, 25, 7, 12, 17, 26, 7, 27, 7, 21, 28, 12, 7, 29, 30, 31, 17, 21, 7, 32, 24, 33, 17, 12, 7, 34, 7, 12, 35, 36, 24, 27, 7, 21, 17, 37, 7, 38, 7, 12, 39, 21, 40, 27, 7, 41, 42, 12, 7, 43, 24, 12, 17, 33, 7, 44, 40, 21, 17, 12, 24, 45, 7, 46, 35

Offset

1,2

Comments

Restricted growth sequence transform of ordered 4-tuple [A046523(n), A007814(n), A007949(n), A112765(n)].

For all i, j:

A379000(i) = A379000(j) => a(i) = a(j),

a(i) = a(j) => A358230(i) = A358230(j),

a(i) = a(j) => A379002(i) = A379002(j),

a(i) = a(j) => A379005(i) = A379005(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Prog

(PARI)
up_to = 100000;
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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
v379001 = rgs_transform(vector(up_to, n, [A046523(n), valuation(n, 2), valuation(n, 3), valuation(n, 5)]));
A379001(n) = v379001[n];

Crossrefs

Cf. A046523, A007814, A007949, A112765.

Cf. A358230, A379000, A379002, A379005.

Sequence in context: A275987 A048893 A330814 * A379000 A305903 A305904

Adjacent sequences: A378998 A378999 A379000 * A379002 A379003 A379004

Keyword

nonn

Author

Antti Karttunen, Dec 15 2024

Status

approved