The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A291751 Lexicographically earliest such sequence a that a(i) = a(j) => A003557(i) = A003557(j) and A048250(i) = A048250(j), for all i, j. 14
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 6, 11, 12, 13, 13, 14, 10, 15, 16, 17, 18, 19, 13, 20, 21, 22, 23, 24, 25, 26, 18, 27, 28, 29, 28, 30, 31, 32, 33, 34, 22, 35, 36, 37, 38, 26, 28, 39, 40, 41, 26, 42, 29, 43, 26, 44, 45, 46, 32, 47, 48, 35, 49, 50, 51, 52, 53, 54, 35, 52, 26, 55, 56, 57, 58, 59, 35, 60, 45, 61, 62, 63, 51, 64, 65, 66, 67, 68, 46, 69, 70, 47, 71 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Restricted growth sequence transform of A291750, which means that this is the lexicographically least sequence a, such that for all i, j: a(i) = a(j) <=> A291750(i) = A291750(j) <=> A003557(i) = A003557(j) and A048250(i) = A048250(j). That this is equal to the definition given in the title follows because any such lexicographically least sequence satisfying relation <=> is also the least sequence satisfying relation => with the same parameters. Sigma (A000203) and psi (A001615) are functions of this sequence. See comments in A291750 for the reason. For example, to find the value of A001615(n) when we know just a(n), but without knowing n, let m be the least i for which a(i) = a(n); then A001615(n) = A003991(A291750(m)) = A003557(m) * A048250(m). LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 PROG (PARI) 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 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)); v291751 = rgs_transform(vector(65537, n, A291750(n))); A291751(n) = v291751[n]; CROSSREFS Cf. A001615, A003557, A048250, A291750, A291752, A294877, A295300, A295886, A295887, A295888, A319698, A322021. Differs from A286603 for the first time at n = 25, where a(25) = 21, while A286603(25) = 14. Sequence in context: A171060 A254596 A286603 * A275987 A048893 A330814 Adjacent sequences:  A291748 A291749 A291750 * A291752 A291753 A291754 KEYWORD nonn AUTHOR Antti Karttunen, Sep 06 2017 EXTENSIONS Name changed and comments added by Antti Karttunen, Nov 24 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)