The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A363170 The number of powerful abundant numbers (A363169) not exceeding 10^n. 1
 0, 3, 23, 82, 297, 1000, 3268, 10534, 33799, 107901, 343155, 1090189, 3460380, 10970774, 34749182, 109991778, 348006756, 1101058505, 3483105232, 11017518803 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The ratios a(n)/A118896(n) seem to converge to a positive value as n grows: for n = 14..20 they are 0.506417..., 0.506728..., 0.506863..., 0.506890..., 0.506987..., 0.507059..., 0.507120... . Conjecture: the asymptotic relative density of the abundant numbers within the powerful numbers exists and equals 0.507... . LINKS Table of n, a(n) for n=1..20. EXAMPLE a(2) = 3 since there are 3 powerful abundant numbers not exceeding 10^2: 36, 72 and 100. MATHEMATICA seq[nmax_] := Module[{c = 0, p = 10, k = 1, kmax = 10^nmax, s = {}}, While[k <= kmax, If[DivisorSigma[-1, k] > 2 && Min[FactorInteger[k][[;; , 2]]] > 1, c++]; If[k == p, AppendTo[s, c]; p *= 10]; k++]; s]; seq[5] PROG (PARI) is(n) = { my(f = factor(n)); n > 1 && vecmin(f[, 2]) > 1 && sigma(f, -1) > 2; } \\ A363169 lista(nmax) = {my(c = 0, p = 10, k = 1, kmax = 10^nmax); while(k <= kmax, if(is(k), c++); if(k == p, print1(c, ", "); p *= 10); k++); } CROSSREFS Cf. A001694, A005101, A118896, A302992, A363169. Sequence in context: A126335 A256329 A196649 * A357738 A027701 A201482 Adjacent sequences: A363167 A363168 A363169 * A363171 A363172 A363173 KEYWORD nonn,more AUTHOR Amiram Eldar, May 19 2023 STATUS approved

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

Last modified September 15 20:25 EDT 2024. Contains 375955 sequences. (Running on oeis4.)