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A080258 Either 4th power of a prime, or product of a prime and the square of a different prime. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Union of A030514 and A054753; A080256(a(n)) = 5.

Or, the numbers n such that 8=number of perfect partitions of n. - Juri-Stepan Gerasimov, Sep 26 2009

Numbers such that the sum of the number of divisors of their aliquot parts is two times the number of their divisors. [Paolo P. Lava, Apr 22 2016]

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..10000

FORMULA

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

EXAMPLE

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

MAPLE

with(numtheory): P:=proc(q) local a, k, n;  for n from 2 to q do a:=sort([op(divisors(n))]);

if 2*tau(n)= add(tau(a[k]), k=1..nops(a)-1) then print(n); fi; od; end: P(10^7);  # Paolo P. Lava, Apr 22 2016

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: A272861 A192690 A064499 * A054290 A107308 A051518

Adjacent sequences:  A080255 A080256 A080257 * A080259 A080260 A080261

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 10 2003

STATUS

approved

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Last modified June 17 19:05 EDT 2019. Contains 324198 sequences. (Running on oeis4.)