

A126098


Where records occur in A018892.


12



1, 2, 4, 6, 12, 24, 30, 60, 120, 180, 210, 360, 420, 840, 1260, 1680, 2520, 4620, 7560, 9240, 13860, 18480, 27720, 55440, 83160, 110880, 120120, 180180, 240240, 360360, 720720, 1081080, 1441440, 1801800, 2042040, 2882880, 3063060, 4084080, 5405400, 6126120, 12252240, 18378360, 24504480
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OFFSET

1,2


COMMENTS

Remarkably similar to but ultimately different from A018894.  Jorg Brown and N. J. A. Sloane, Mar 06 2007
This sequence represents "where records occur" for a number of sequences in addition to A018892 including the following: A015995, A015996, A015999, A016001, A016002, A016003, A016005, A016006, A016007, A016008, A016009, A048691, A048785, A063647, A117677, A144943.  Ray Chandler, Dec 04 2008
Subsequence of A025487.  Ray Chandler, Sep 05 2008
Also recordsetting elements of tau(n^2) (just as A002182 gives the recordsetting elements of tau(n)). The point is that A018892 is (tau(n^2) + 1)/2. As tau(n^2) is odd, the recordsetting elements of A018892 are also the record setting elements of tau(n^2).  Allen Tracht, Jan 20 2009


LINKS

Ray Chandler, Table of n, a(n) for n = 1..582
Jorg Brown, Comparison of records in sigma(n)/phi(n) and A018892


PROG

(C++)
// This C++ program generates the sequence of n for which A018892 sets a new record. It takes one argument, defaulting to 300, which is the maximum record that it's looking for.
int main(int argc, char *argv[]) { int limit = (argc != 2) ? 300 : atoi(argv[1]); int maxsol = 0; for (unsigned int n = 2*3*5;; n += 2*3*5) { int numsol = 0; for (uint64_t x = n + 1; x <= n + n; ++x) { uint64_t y = x * n / (x  n); if (y * (x  n) == x * n) { numsol++; } } if (numsol > maxsol) { printf("New max n=%d sols=%d ", n, numsol); maxsol = numsol; } if (numsol >= limit) break; } } // Jorg Brown (jorg(AT)google.com), Mar 05 2007


CROSSREFS

Cf. A018892, A126097. Equals A117010(n) + 1.
Sequence in context: A097212 A266228 A265719 * A018894 A168264 A282472
Adjacent sequences: A126095 A126096 A126097 * A126099 A126100 A126101


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Mar 05 2007


EXTENSIONS

More terms from Jorg Brown (jorg(AT)google.com) and T. D. Noe, Mar 05 2007
a(27) corrected by hupo001(AT)gmail.com, Jan 10 2008


STATUS

approved



