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A320943 Numbers that have exactly 26 representations as a k-gonal number, P(n,k) = n*((k-2)*n - (k-4))/2, k and n >= 3. 6


%S 1559439365121,2468046593376,7760419091425

%N Numbers that have exactly 26 representations as a k-gonal number, P(n,k) = n*((k-2)*n - (k-4))/2, k and n >= 3.

%H Hugh Erling, <a href="/A320943/a320943.txt">Python program</a>

%e a(1): 1559439365121 has representations P(n,k) = P(3, 519813121708)=P(6, 103962624343)=P(9, 43317760144)=P(11, 28353443004)=P(18, 10192414153)=P(27, 4442847196)=P(33, 2953483648)=P(57, 977092336)=P(66, 727011361)=P(69, 664722664)=P(81, 481308448)=P(86, 426659199)=P(129, 188885584)=P(131, 183140268)=P(171, 107288572)=P(209, 71744544)=P(237, 55761976)=P(414, 18240979)=P(473, 13969968)=P(513, 11874388)=P(711, 6178324)=P(729, 5876784)=P(1881, 881968)=P(3537, 249376)=P(16899, 10924)=P(720981, 8).

%e a(2): 2468046593376 has representations P(n,k) = P(3, 822682197793)=P(6, 164536439560)=P(12, 37394645356)=P(18, 16131023488)=P(24, 8942197804)=P(26, 7593989520)=P(39, 3330697159)=P(42, 2866488496)=P(56, 1602627660)=P(72, 965589436)=P(84, 707988124)=P(96, 541238290)=P(116, 370021980)=P(126, 313402744)=P(392, 32204796)=P(416, 28591830)=P(576, 14903665)=P(647, 11809911)=P(783, 8061483)=P(936, 5640220)=P(1827, 1479601)=P(2912, 582306)=P(4302, 266776)=P(5823, 145603)=P(7056, 99160)=P(145551, 235).

%e a(3): 7760419091425 has representations P(n,k) = P(5, 776041909144)=P(7, 369543766260)=P(10, 172453757589)=P(13, 99492552456)=P(19, 45382567788)=P(25, 25868063640)=P(35, 13042721164)=P(37, 11652280920)=P(49, 6598995828)=P(55, 5225871444)=P(65, 3730970719)=P(82, 2336771785)=P(143, 764347396)=P(145, 743335164)=P(154, 658723293)=P(205, 371134344)=P(290, 185190769)=P(325, 147396376)=P(475, 68935548)=P(1225, 10351368)=P(1378, 8179601)=P(1729, 5194893)=P(2755, 2045644)=P(7585, 269814)=P(1969825, 6)=P(3939649, 3).

%o (PARI) See _Hugh Erling_, Oct 29 2018 link.

%Y Cf. A057145, A063778, A129654, A139601, A177029, A195527, A195528.

%Y A subsequence of A090466.

%K nonn,more,bref

%O 1,1

%A _Hugh Erling_, Oct 24 2018

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Last modified April 12 19:50 EDT 2021. Contains 342932 sequences. (Running on oeis4.)