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A306986 Number of primitive abundant numbers (A071395) < 10^n. 0
0, 3, 14, 98, 441, 1734, 8667, 41653, 213087 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..9.

Michael R. Avidon, On the distribution of primitive abundant numbers, Acta Arithmetica, Vol. 77, No. 2 (1996), pp. 195-205.

Paul Erdős, On primitive abundant numbers, J. London Math. Soc., Volume s1-10, Issue 1 (1935), pp. 49-58, alternative link.

Aleksandar Ivić, The distribution of primitive abundant numbers, Studia Sci. Math. Hungar., Vol. 20 (1985), pp. 183-187.

EXAMPLE

There are 3 terms of A071395 below 100 (20, 70, and 88), thus a(2) = 3.

MATHEMATICA

paQ[n_] := DivisorSigma[1, n] > 2n && Times @@ Boole@ Map[DivisorSigma[1, #] < 2 # &, Most@ Divisors@ n] == 1;  c = 0; k = 1;  seq={}; Do[ While[ k < 10^n, If[ paQ[k], c++ ]; k ++]; AppendTo[seq, c], {n, 1, 5}]; seq (* after Michael De Vlieger at A071395 *)

CROSSREFS

Cf. A071395, A302992.

Sequence in context: A136461 A276747 A007470 * A074515 A038051 A132008

Adjacent sequences:  A306983 A306984 A306985 * A306987 A306988 A306989

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Mar 18 2019

STATUS

approved

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Last modified November 14 19:55 EST 2019. Contains 329128 sequences. (Running on oeis4.)