A261256 Let S_k denote the sequence of numbers j such that A001222(j) - A001221(j) = k. Then a(n) is the n-th term of S_n.

4, 24, 72, 160, 432, 896, 2592, 5632, 12800, 26624, 61440, 124416, 278528, 622592, 1376256, 2949120, 5971968, 12058624, 25690112, 60817408, 130023424, 262144000, 528482304, 1107296256, 2264924160, 4586471424, 9395240960, 19864223744, 40265318400, 83751862272

Offset

1,1

Comments

S_0 would correspond to the squarefree numbers (A005117), that is, numbers j such that A001222(j) = A001221(j). Note that S_0 is excluded from the scheme. - Michel Marcus, Sep 21 2015

Links

Charlie Neder, Table of n, a(n) for n = 1..500

Formula

a(n+1) > 2*a(n).

a(n) >= 2^prime(n) for n < 5.

a(n) = A257851(n,n-1). - Reinhard Zumkeller, Nov 29 2015

a(n) = b(n)*2^(n+1), where b(n) consists of the values of k/2^excess(k) over odd k, sorted in ascending order. In particular, a(n) <= prime(n)*2^(n+1), with equality only when n = 2. - Charlie Neder, Jan 31 2019

Example

For n = 1, S_1 = {4, 9, 12, 18, 20, 25, ...}, so a(1) = S_1(1) = 4.
For n = 2, S_2 = {8, 24, 27, 36, 40, 54, ...}, so a(2) = S_2(2) = 24.
For n = 3, S_3 = {16, 48, 72, 80, 81, 108, ...}, so a(3) = S_3(3) = 72.
For n = 4, S_4 = {32, 96, 144, 160, 216, 224, ...}, so a(4) = S_4(4) = 160.
For n = 5, S_5 = {64, 192, 288, 320, 432, 448, ...}, so a(5) = S_5(5) = 432.

Mathematica

OutSeq = {}; For[i = 1, i <= 16, i++, l = Select[Range[10^2*2^i], PrimeOmega[#] - PrimeNu[#] == i &]; AppendTo[OutSeq, l[[i]]]]; OutSeq

Prog

(PARI) a(n) = {ik = 1; nbk = 0; while (nbk != n, ik++; if (bigomega(ik) == omega(ik) + n, nbk++); ); ik; } \\ Michel Marcus, Oct 06 2015
(Haskell)
a261256 n = a257851 n (n - 1)  -- Reinhard Zumkeller, Nov 29 2015

Crossrefs

Cf. A001221, A001222.

Cf. A060687, A195086, A195087, A195088, A195089, A195090, A195091, A195092, A195093.

Cf. A046660, A257851, A264959.

Sequence in context: A336039 A364600 A181617 * A011915 A199904 A250132

Adjacent sequences: A261253 A261254 A261255 * A261257 A261258 A261259

Keyword

nonn

Author

Carlos Eduardo Olivieri, Aug 12 2015

Extensions

a(17)-a(21) from Jon E. Schoenfield, Sep 12 2015

More terms from Charlie Neder, Jan 31 2019

Status

approved