login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A302994 Number of bi-unitary abundant numbers < 10^n. 0
0, 14, 147, 1553, 15450, 155395, 1549818, 15498814, 155079196, 1550331185, 15503061466, 155037242668, 1550370696100, 15503650949671, 155036854371220, 1550366484701654, 15503648102080675 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..17.

FORMULA

Conjecture: Lim_{n->oo} a(n)/10^n = 0.15... is the density of bi-unitary abundant numbers.

MATHEMATICA

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bsigma[m_] :=

DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; babQ[n_] := bsigma[n] > 2 n; c = 0; k = 1; seq={}; Do[While[k < 10^n, If[babQ[k], c++]; k++]; AppendTo[seq, c], {n, 1, 5}]; seq

PROG

(PARI) biusigma(n) = {f = factor(n); for (i=1, #f~, p = f[i, 1]; e = f[i, 2]; f[i, 1] = if (e % 2, (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1) -p^(e/2)); f[i, 2] = 1; ); factorback(f); }

a(n) = sum(k=1, 10^n-1, biusigma(k) > 2*k); \\ Michel Marcus, Apr 17 2018

CROSSREFS

Cf. A188999, A292982, A302992.

Sequence in context: A132934 A027473 A002451 * A207259 A016170 A081201

Adjacent sequences:  A302991 A302992 A302993 * A302995 A302996 A302997

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Apr 17 2018

EXTENSIONS

a(8)-a(17) from Hiroaki Yamanouchi, Aug 24 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 21 06:40 EST 2019. Contains 320371 sequences. (Running on oeis4.)