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A145551 Numbers n such that product of divisors of n / sum of divisors of n is an integer. 6
1, 6, 28, 30, 66, 84, 102, 120, 210, 270, 318, 330, 364, 420, 462, 496, 510, 546, 570, 642, 672, 690, 714, 840, 868, 870, 924, 930, 966, 1080, 1092, 1122, 1320, 1410, 1428, 1488, 1518, 1590, 1638, 1722, 1770, 1782, 1890, 1932, 2040, 2130, 2226, 2280, 2310 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that A007955(n)/A000203(n) is an integer

Numbers such that n^sigma_0(n) is a multiple of sigma_1(n)^2. - Chai Wah Wu, Mar 09 2016

REFERENCES

Zhang Wengpeng : On the divisor products and proper divisor products sequences,Smarandache Notions Journal,Volume 13, Issue 1-2-3(Spring 2002),pp. 128 - 133, ISSN:1084-2810

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..1100

MAPLE

A007955 := proc(n) local dvs, d ; dvs := numtheory[divisors](n) ; mul(d, d=dvs) ; end: A000203 := proc(n) local dvs, d ; dvs := numtheory[divisors](n) ; add(d, d=dvs) ; end: isA145551 := proc(n) RETURN(A007955(n) mod A000203(n) = 0) ; end: for n from 1 to 10000 do if isA145551(n) then printf("%d, ", n) ; fi; od: # R. J. Mathar, Oct 14 2008

MATHEMATICA

spQ[n_]:=Module[{ds=Divisors[n]}, IntegerQ[(Times@@ds)/Total[ds]]]; Select[ Range[2500], spQ] (* Harvey P. Dale, Jun 26 2012 *)

PROG

(Python)

from sympy import divisor_sigma

A145551_list = [n for n in range(1, 10**3) if not n**divisor_sigma(n, 0) % divisor_sigma(n, 1)**2] # Chai Wah Wu, Mar 09 2016

CROSSREFS

Cf. A000203, A007955, A140480

Sequence in context: A211679 A261868 A105402 * A259917 A083865 A185351

Adjacent sequences:  A145548 A145549 A145550 * A145552 A145553 A145554

KEYWORD

easy,nonn

AUTHOR

Ctibor O. Zizka, Oct 13 2008

EXTENSIONS

90, 96, 108, 126, 132, 140 removed, extended by R. J. Mathar, Oct 14 2008

STATUS

approved

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Last modified February 25 16:14 EST 2018. Contains 299653 sequences. (Running on oeis4.)