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 A304978 Numbers that can be expressed in more than one way as 6xy + x + y with x >= y > 0. 1
 106, 155, 197, 204, 253, 288, 302, 351, 379, 400, 421, 449, 470, 498, 504, 535, 547, 554, 561, 596, 645, 652, 687, 694, 704, 729, 743, 779, 782, 792, 820, 834, 841, 873, 890, 904, 925, 939, 953, 988, 1016, 1029, 1037, 1042, 1054, 1079, 1086, 1107, 1121, 1135, 1184, 1198, 1204, 1211, 1219, 1233, 1254, 1276, 1282, 1289, 1329 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Is it possible to find a closed form formula for this sequence? Numbers k such that 6*k+1 has at least 5 divisors == 1 (mod 6). - Robert Israel, Jan 20 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 106 is in this sequence because 106 can be expressed in two different ways as 6xy + x + y: 6*8*2 + 8 + 2 and 6*15*1 + 15 + 1. MAPLE filter:= proc(n) nops(select(t -> t mod 6 =1, numtheory:-divisors(6*n+1)))>= 5 end proc: select(filter, [\$1..2000]); # Robert Israel, Jan 20 2019 MATHEMATICA Select[Range[1329], 2 == Length@ FindInstance[ 6*x*y+x+y == # && x >= y > 0, {x, y}, Integers, 2] &] (* Giovanni Resta, May 29 2018 *) PROG (PYTHON) # Finding duplicates in matrix A where {a_ij}=6*i*j+i+j def cuenta(a):     repa=[]     dupo=[]     k=0     sumo=0     while k1:             repa.append(a[k])             dupo.append(dupa)             sumo +=(dupa-1)         k +=dupa     return repa, dupo, sumo kuno = [] for k in range(1, a + 1):     for j in range(1, k + 1):         m=6 * k * j + k + j         if m <= NN // 6: kuno.append(m) kuno=sorted(kuno) repkuno, dupkuno, suno= cuenta(kuno) print(repkuno) # #END (PARI) is(n) = my(i=0); for(x=1, n, for(y=1, x, if(n==6*x*y+x+y, i++; if(i==2, return(1))))); 0 \\ Felix FrÃ¶hlich, May 29 2018 CROSSREFS Subsequence of A067611. Sequence in context: A163625 A070796 A045093 * A078776 A188006 A160725 Adjacent sequences:  A304975 A304976 A304977 * A304979 A304980 A304981 KEYWORD nonn AUTHOR Pedro Caceres, May 22 2018 STATUS approved

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Last modified May 31 19:40 EDT 2020. Contains 334748 sequences. (Running on oeis4.)