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 A271382 Least k with precisely n partitions k = x + y satisfying d(k) = d(x) + d(y), where d(k) is the number of divisors of k. 2
 2, 14, 10, 26, 44, 45, 126, 68, 99, 104, 162, 117, 98, 124, 232, 164, 148, 200, 260, 333, 231, 244, 248, 297, 273, 284, 315, 406, 332, 345, 385, 430, 344, 399, 388, 436, 429, 488, 465, 495, 472, 525, 561, 555, 621, 556, 632, 604, 652, 712, 536, 693, 735, 675 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Paolo P. Lava, Table of n, a(n) for n = 1..1200 EXAMPLE d(10) = d(1) + d(9) = d(3) + d(7) = d(5) + d(5) = 4 and 10 is the least number with 3 partitions of two numbers with this property: therefore a(3) = 10; d(126) = d(21) + d(105) = d(22) + d(104) = d(28) + d(98) = d(38) + d(33) = d(40) + d(86) = d(50) + d(76) = d(63) + d(63) = 12 and 126 is the least number with 7 partitions of two numbers with this property: therefore a(7) = 126. MAPLE with(numtheory): P:=proc(q) local a, h, k, n; for h from 1 to q do for n from 2*h to q do a:=0; for k from 1 to trunc(n/2) do if tau(n)=tau(k)+tau(n-k) then a:=a+1; fi; od; if a=h then print(n); break; fi; od; od; end: P(10^6); MATHEMATICA nn = 10^3; Table[SelectFirst[Range@ nn, Function[k, With[{e = DivisorSigma[0, k]}, Count[Transpose@ {Range[k - 1, Ceiling[k/2], -1], Range@ Floor[k/2]}, x_ /; Total@ DivisorSigma[0, x] == e] == n]]], {n, 54}] (* Michael De Vlieger, Apr 06 2016 *) PROG (PARI) isok(k, n) = {my(nb = 0, tau = numdiv(k)); for (j=1, k\2, if (numdiv(j)+numdiv(k-j) == tau, nb++); if (nb > n, return (0)); ); nb == n; } a(n) = {k=2; while (!isok(k, n), k++); k; } \\ Michel Marcus, Apr 07 2016 CROSSREFS Cf. A000005, A211224, A271384. Sequence in context: A191995 A168207 A082609 * A158787 A174706 A072163 Adjacent sequences:  A271379 A271380 A271381 * A271383 A271384 A271385 KEYWORD nonn,easy AUTHOR Paolo P. Lava, Apr 06 2016 STATUS approved

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Last modified January 19 20:01 EST 2019. Contains 319309 sequences. (Running on oeis4.)