A126098 Where records occur in A018892.

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

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 record-setting elements of tau(n^2) (just as A002182 gives the record-setting elements of tau(n)). The point is that A018892 is (tau(n^2) + 1)/2. As tau(n^2) is odd, the record-setting 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: A362081 A265719 A378630 * A018894 A340816 A168264

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