A190464 Numbers with prime factorization p^4*q^6.

5184, 11664, 40000, 153664, 250000, 455625, 937024, 1265625, 1750329, 1827904, 1882384, 5345344, 8340544, 9529569, 10673289, 17909824, 20820969, 28344976, 37515625, 45265984, 59105344, 60886809, 73530625, 77228944, 95004009, 119946304, 143496441, 180848704, 204004089, 218803264

Offset

1,1

Comments

A subsequence of A175745 (Numbers with 35 divisors).

First different term in A175745 is 17179869184(=2^34).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Will Nicholes, Prime Signatures

Index to sequences related to prime signature

Formula

Sum_{n>=1} 1/a(n) = P(4)*P(6) - P(10) = A085964 * A085966 - P(10) = 0.000320..., where P is the prime zeta function. - Amiram Eldar, Jul 06 2020

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={4, 6}; Select[Range[50000000], f] (*and*) lst={}; Do[Do[If[n!=m, AppendTo[lst, Prime[n]^6*Prime[m]^4]], {n, 50}], {m, 50}]; Take[Union@lst, 50]

Prog

(PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\16)^(1/6), t=p^6; forprime(q=2, (lim\t)^(1/4), if(p==q, next); listput(v, t*q^4))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 24 2011

Crossrefs

Cf. A030629, A179692, A179699, A179705, A175745.

Cf. A085964, A085966.

Sequence in context: A185485 A061050 A175745 * A031570 A066167 A247265

Adjacent sequences: A190461 A190462 A190463 * A190465 A190466 A190467

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 10 2011

Status

approved