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%I #18 Mar 13 2019 23:40:31
%S 1,2,4,6,12,24,30,60,120,180,210,360,420,840,1260,1680,2520,4620,7560,
%T 9240,13860,18480,27720,55440,83160,110880,120120,180180,240240,
%U 360360,720720,1081080,1441440,1801800,2042040,2882880,3063060,4084080,5405400,6126120,12252240,18378360,24504480
%N Where records occur in A018892.
%C Remarkably similar to but ultimately different from A018894. - Jorg Brown and _N. J. A. Sloane_, Mar 06 2007
%C 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
%C Subsequence of A025487. - _Ray Chandler_, Sep 05 2008
%C 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
%H Ray Chandler, <a href="/A126098/b126098.txt">Table of n, a(n) for n = 1..582</a>
%H Jorg Brown, <a href="/A018894/a018894.txt">Comparison of records in sigma(n)/phi(n) and A018892</a>
%o (C++)
%o // 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.
%o 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
%Y Cf. A018892, A126097. Equals A117010(n) + 1.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Mar 05 2007
%E More terms from Jorg Brown (jorg(AT)google.com) and _T. D. Noe_, Mar 05 2007
%E a(27) corrected by hupo001(AT)gmail.com, Jan 10 2008
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