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A369260
Lexicographically earliest infinite sequence such that a(i) = a(j) => A342671(i) = A342671(j) and A349162(i) = A349162(j), for all i, j >= 1.
4
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 15, 23, 16, 24, 25, 26, 27, 28, 21, 29, 30, 31, 30, 32, 33, 34, 26, 35, 36, 37, 38, 39, 40, 28, 30, 41, 42, 43, 44, 45, 46, 47, 44, 48, 49, 50, 51, 52, 53, 37, 54, 55, 56, 57, 58, 59, 60, 57, 44, 61, 62, 63, 41, 64, 60, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 65, 79, 57
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of the ordered pair [A342671(n), A349162(n)], or equally, of the pair [A000203(n), A342671(n)], or equally, of the pair [A000203(n), A349162(n)].
For all i, j >= 1:
A369259(i) = A369259(j) => a(i) = a(j) => A286603(i) = A286603(j).
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; };
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A342671(n) = gcd(sigma(n), A003961(n));
Aux369260(n) = { my(u=A342671(n)); [u, sigma(n)/u]; };
v369260 = rgs_transform(vector(up_to, n, Aux369260(n)));
A369260(n) = v369260[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 25 2024
STATUS
approved