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A285457 Least number k such that the absolute value of the difference between the number of divisors of k and k-1 is equal to n. 3
3, 2, 6, 17, 12, 25, 24, 37, 48, 325, 60, 144, 120, 121, 168, 289, 180, 529, 240, 577, 481, 361, 360, 900, 960, 961, 721, 5185, 720, 841, 840, 2401, 1261, 17425, 1260, 14641, 1680, 1681, 2161, 8281, 2880, 3600, 6480, 7057, 2520, 6241, 2521, 82945, 6481, 225625, 7200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Odd indexed terms are equal to a square or to a square plus one. - Giovanni Resta, Apr 28 2017

LINKS

Paolo P. Lava and Giovanni Resta, Table of n, a(n) for n = 0..1000 (first 150 terms from Paolo P. Lava)

FORMULA

Least solutions of the equation abs(A000005(k) - A000005(k-1)) = n.

EXAMPLE

a(9) = 325 because 324 has 15 divisors (1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324), 325 has 6 divisors (1, 5, 13, 25, 65, 325) and 15 - 6 = 9.

MAPLE

with(numtheory): P:=proc(q) local a, b, k, v; v:=array(0..200);

for k from 0 to 200 do v[k]:=0; od; a:=1;

for k from 2 to q do b:=tau(k); if v[abs(b-a)]=0 then v[abs(b-a)]:=k; fi; a:=b; od; k:=0;

while v[k]>0 do print(v[k]); k:=k+1; od; print(); end: P(3*10^5);

MATHEMATICA

s = DivisorSigma[0, #] &@ Range[10^6]; 1 + First /@ Values@ KeySort@ PositionIndex@ Flatten@ Map[Abs@ Differences@ # &, Partition[s, 2, 1]] (* Michael De Vlieger, Apr 26 2017, Version 10 *)

CROSSREFS

Cf. A000005, A051950, A086550 (without abs), A285787 (with bigomega).

Sequence in context: A248982 A289069 A074718 * A007812 A276225 A082561

Adjacent sequences:  A285454 A285455 A285456 * A285458 A285459 A285460

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Apr 26 2017

STATUS

approved

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Last modified September 16 12:34 EDT 2019. Contains 327098 sequences. (Running on oeis4.)