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 A324976 Rank of the n-th primary Carmichael number. 5
 12, 8, 18, 12, 52, 52, 20, 32, 16, 54, 8, 36, 124, 34, 12, 72, 96, 26, 28, 76, 98, 1804, 108, 124, 18, 72, 172, 120, 10, 104, 32, 244, 130, 376, 18, 92, 780, 36, 172, 92, 284, 24, 198, 12, 244, 64, 234, 340, 100, 284, 24, 124, 44, 518, 364, 16, 82, 148, 8, 206 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A324974 for definition and explanation of rank of a special polygonal number, hence of rank of a primary Carmichael number A324316 by Kellner and Sondow 2019. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Bernd C. Kellner and Jonathan Sondow, On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base-p digits, Integers 21 (2021), #A52, 21 pp.; arXiv:1902.10672 [math.NT], 2019. Bernd C. Kellner, On primary Carmichael numbers, Integers 22 (2022), #A38, 39 pp.; arXiv:1902.11283 [math.NT], 2019. Wikipedia, Polygonal number FORMULA a(n) = 2+2*((m/p)-1)/(p-1), where m = A324316(n) and p is its greatest prime factor. Hence a(n) is even; see Formula in A324975. EXAMPLE If m = A324316(1) = 1729 = 7*13*19, then p = 19, so a(1) = 2+2*((1729/19)-1)/(19-1) = 12. MATHEMATICA SD[n_, p_] := If[n < 1 || p < 2, 0, Plus @@ IntegerDigits[n, p]]; LP[n_] := Transpose[FactorInteger[n]][]; TestCP[n_] := (n > 1) && SquareFreeQ[n] && VectorQ[LP[n], SD[n, #] == # &]; T = Select[Range[1, 10^7, 2], TestCP[#] &]; GPF[n_] := Last[Select[Divisors[n], PrimeQ]]; Table[2 + 2*(T[[i]]/GPF[T[[i]]] - 1)/(GPF[T[[i]]] - 1), {i, Length[T]}] CROSSREFS Subsequence of A324975 (rank of the n-th Carmichael number A002997) and of A324974 (rank of the n-th special polygonal number A324973). Cf. also A324316, A324972. Sequence in context: A071279 A118656 A094332 * A261402 A307171 A040134 Adjacent sequences: A324973 A324974 A324975 * A324977 A324978 A324979 KEYWORD nonn,base AUTHOR Bernd C. Kellner and Jonathan Sondow, Mar 24 2019 EXTENSIONS More terms from Amiram Eldar, Mar 27 2019 STATUS approved

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Last modified November 29 07:03 EST 2023. Contains 367429 sequences. (Running on oeis4.)