This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319582 Square array T(n, k) = 2 ^ (Sum_{p prime} [v_p(n) >= v_p(k) > 0]) read by antidiagonals up, where [] is the Iverson bracket and v_p is the p-adic valuation, n >= 1, k >= 1. 1
 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS T(n, k) is the number of integers located on the sphere with center n and radius log(k), when the metric is given by log(A089913). T(., k) is multiplicative and k-periodic. T(n, .) is multiplicative and n^2-periodic. LINKS FORMULA T(n, k) = card({x; d(n, x) = log(k)}), if d denotes log(A089913(., .)), which is a metric. T(n, k) = 2 ^ (Sum_{p prime} [v_p(n) >= v_p(k) > 0]). a(n) = 2 ^ A319581(n). T(n, n) = 2 ^ A001221(n) = A034444(n). EXAMPLE T(60, 50) = T(2^2 * 3^1 * 5^1, 2^1 * 5^2)   = T(2^2, 2^1) * T(3^1, 3^0) * T(5^1, 5^2)   = 2^[2 >= 1 > 0] * 2^[1 >= 0 > 0] * 2^[1 >= 2 > 0])   = 2^1 * 2^0 * 2^0 = 2 * 1 * 1 = 2. Array begins:      k =                 1 1 1    n   1 2 3 4 5 6 7 8 9 0 1 2    =  ------------------------    1 | 1 1 1 1 1 1 1 1 1 1 1 1    2 | 1 2 1 1 1 2 1 1 1 2 1 1    3 | 1 1 2 1 1 2 1 1 1 1 1 2    4 | 1 2 1 2 1 2 1 1 1 2 1 2    5 | 1 1 1 1 2 1 1 1 1 2 1 1    6 | 1 2 2 1 1 4 1 1 1 2 1 2    7 | 1 1 1 1 1 1 2 1 1 1 1 1    8 | 1 2 1 2 1 2 1 2 1 2 1 2    9 | 1 1 2 1 1 2 1 1 2 1 1 2   10 | 1 2 1 1 2 2 1 1 1 4 1 1   11 | 1 1 1 1 1 1 1 1 1 1 2 1   12 | 1 2 2 2 1 4 1 1 1 2 1 4 MATHEMATICA F[n_] := If[n == 1, {}, FactorInteger[n]] V[p_] := If[KeyExistsQ[#, p], #[p], 0] & PreT[n_, k_] := Module[{fn = F[n], fk = F[k], p, an = <||>, ak = <||>, w},   p = Union[First /@ fn, First /@ fk];   (an[#[[1]]] = #[[2]]) & /@ fn;   (ak[#[[1]]] = #[[2]]) & /@ fk;   w = ({V[#][an], V[#][ak]}) & /@ p;   Select[w, (#[[1]] >= #[[2]] > 0) &]   ] T[n_, k_] := 2^Length[PreT[n, k]] A004736[n_] := Binomial[Floor[3/2 + Sqrt[2*n]], 2] - n + 1 A002260[n_] := n - Binomial[Floor[1/2 + Sqrt[2*n]], 2] a[n_] := T[A004736[n], A002260[n]] Table[a[n], {n, 1, 90}] PROG (PARI) maxp(n) = if (n==1, 1, vecmax(factor(n)[, 1])); T(n, k) = {pmax = max(maxp(n), maxp(k)); x = 0; forprime(p=2, pmax, if ((valuation(n, p) >= valuation(k, p)) && (valuation(k, p) > 0), x ++); ); 2^x; } \\ Michel Marcus, Oct 28 2018 CROSSREFS Cf. A319581 (an additive variant). Cf. A001221, A034444, A089913. Sequence in context: A060209 A037830 A174353 * A187447 A146292 A139039 Adjacent sequences:  A319579 A319580 A319581 * A319583 A319584 A319585 KEYWORD nonn,tabl AUTHOR Luc Rousseau, Sep 24 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 10 12:15 EST 2019. Contains 329895 sequences. (Running on oeis4.)