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A290945 Triangular Carmichael numbers. 2
561, 8911, 10585, 41041, 115921, 314821, 334153, 6313681, 8134561, 14913991, 32914441, 60957361, 67902031, 135556345, 289766701, 321197185, 329769721, 368113411, 471905281, 765245881, 842202361, 962442001, 1507746241, 2489462641, 2588653081, 3104207821 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A000217 and A002997.

The least triangular Carmichael numbers with the number of prime factors = 3, 4, 5, 6, 7, ... are: 561, 41041, 765245881, 321197185, 1583892181303201, ...

The number of terms below 10^k for k = 3, 4, ... are: 1, 2, 4, 7, 9, 13, 22, 32, 53, 77, 137, 211, 358, 545, 879, 1423, ...

Jonathan Vos Post discovered in 2004 that a(21) = 842202361 = A000217(41041) = A002817(286) is also a doubly triangular Carmichael number. The next number with this property is a(1108) = 292800629576356021 = A000217(765245881) = A002817(39121) (41041 and 765245881 are triangular Carmichael numbers that are also indices of triangular numbers that are also Carmichael numbers).

LINKS

Table of n, a(n) for n=1..26.

Jonathan Vos Post, Table of Figurate Numbers, Sorted, Through 10,000.

EXAMPLE

8911 = A000217(133) = A002997(7) therefore 8911 is in the sequence.

MATHEMATICA

seqQ[n_]:=IntegerQ[Sqrt[8n+1]] && !PrimeQ[n] && (Mod[n, CarmichaelLambda[n]] == 1); Select[Range[10^6], seqQ]

CROSSREFS

Cf. A000217, A002817, A002997.

Sequence in context: A290692 A293622 A207080 * A063400 A141706 A290485

Adjacent sequences:  A290942 A290943 A290944 * A290946 A290947 A290948

KEYWORD

nonn

AUTHOR

Amiram Eldar, Aug 14 2017

STATUS

approved

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Last modified February 22 12:00 EST 2018. Contains 299452 sequences. (Running on oeis4.)