1,2

Remarkably similar to but ultimately different from A018894. - Jorg Brown and N. J. A. Sloane (njas(AT)research.att.com), Mar 06 2007

Comment from Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 04 2008: This sequence represents "where records occur" for a number of sequences in addition to A018892 including the following: A015995, A015999, A016001, A016002, A016003, A016005, A016006, A016007, A016008, A016009, A048691, A048785, A063647, A117677, A144943.

Subsequence of A025487. [From Ray Chandler (rayjchandler(AT)sbcglobal.net), 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

Ray Chandler, Table of n, a(n) for n=1..103

Jorg Brown, Comparison of records in sigma(n)/phi(n) and A018892

// 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

Cf. A018892, A126097. Equals A117010(n) + 1.

Adjacent sequences: A126095 A126096 A126097 this_sequence A126099 A126100 A126101

Sequence in context: A129301 A066523 A097212 this_sequence A018894 A056795 A141420

nonn

N. J. A. Sloane (njas(AT)research.att.com), Mar 05 2007

More terms from Jorg Brown (jorg(AT)google.com) and T. D. Noe (noe(AT)sspectra.com), Mar 05 2007

a(27) corrected by hupo001(AT)gmail.com, Jan 10 2008