A274365 Numbers n such that n and n+1 both have 30 divisors.

180224, 257499, 579375, 1075599, 1990575, 2353616, 5598800, 10320624, 11560400, 13975983, 16951599, 17213552, 17651600, 17672499, 17784207, 20626991, 20660624, 21041775, 21912848, 22252400, 24533199, 24953103, 26161875, 26604207, 29232175, 29253392

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Mathematica

SequencePosition[Table[If[DivisorSigma[0, n]==30, 1, 0], {n, 3*10^7}], {1, 1}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 10 2018 *)

Prog

(PARI) is(n)=numdiv(n)==30 && numdiv(n+1)==30
(PARI) list(lim)=my(v=List(), t); forprime(p=2, sqrtnint(lim\2, 14), my(p14=p^14); forprime(q=2, lim\p14, if(p==q, next); t=p14*q; if(numdiv(t+1)==30, listput(v, t)); if(numdiv(t-1)==30, listput(v, t-1)))); forprime(p=2, sqrtnint(lim\4, 9), my(p9=p^9); forprime(q=2, sqrtint(lim\p9), if(p==q, next); t=p9*q^2; if(numdiv(t+1)==30, listput(v, t)); if(numdiv(t-1)==30, listput(v, t-1)))); forprime(p=2, sqrtnint(lim\16, 5), my(p5=p^5); forprime(q=2, sqrtnint(lim\p5, 4), if(p==q, next); t=p5*q^4; if(numdiv(t+1)==30, listput(v, t)); if(numdiv(t-1)==30, listput(v, t-1)))); forprime(p=2, sqrtnint(lim\12, 4), my(p4=p^4); forprime(q=2, sqrtint(lim\p4\2), if(p==q, next); my(q2=q^2); forprime(r=2, lim\p4\q2, if(p==r || q==r, next); t=p4*q2*r; if(numdiv(t+1)==30, listput(v, t)); if(numdiv(t-1)==30, listput(v, t-1))))); Set(v)

Crossrefs

Intersection of A005237 and A137493.

Cf. A000005, A274357.

Sequence in context: A060232 A190380 A235716 * A209828 A133541 A145536

Adjacent sequences: A274362 A274363 A274364 * A274366 A274367 A274368

Keyword

nonn

Author

Charles R Greathouse IV, Jun 19 2016

Status

approved