A080258 Either 4th power of a prime, or product of a prime and the square of a different prime.

12, 16, 18, 20, 28, 44, 45, 50, 52, 63, 68, 75, 76, 81, 92, 98, 99, 116, 117, 124, 147, 148, 153, 164, 171, 172, 175, 188, 207, 212, 236, 242, 244, 245, 261, 268, 275, 279, 284, 292, 316, 325, 332, 333, 338, 356, 363, 369, 387, 388, 404, 412, 423, 425, 428, 436

Offset

1,1

Comments

Union of A030514 and A054753.

Numbers that equal the product of the proper divisors of their proper divisors. - Scott R. Shannon, Jul 04 2021

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Formula

A080256(a(n)) = 5.

A002033(a(n)) = 8. - Juri-Stepan Gerasimov, Sep 26 2009

Example

81=3*3*3*3 and 50=2*5*5 are terms.

Mathematica

Module[{nn=20, p4, sdp}, p4=Prime[Range[nn]]^4; sdp=#[[1]] #[[2]]^2&/@ Select[ Tuples[Prime[Range[nn]], 2], #[[1]]!=#[[2]]&]; Take[Join[p4, sdp]// Union, 40]] (* Harvey P. Dale, Jan 31 2021 *)

Prog

(PARI) is(n)=my(f=factor(n)[, 2]~); f==[4] || f==[2, 1] || f==[1, 2] \\ Charles R Greathouse IV, Oct 16 2015

Crossrefs

Cf. A007964, A058080, A001221, A001222, A002033, A006881, A030078.

Sequence in context: A192690 A378082 A064499 * A054290 A107308 A051518

Adjacent sequences: A080255 A080256 A080257 * A080259 A080260 A080261

Keyword

nonn

Author

Reinhard Zumkeller, Feb 10 2003

Status

approved