This site is supported by donations to The OEIS Foundation. Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A245080 Numbers such that omega(a(n)) is a proper divisor of bigomega(a(n)). 2
 4, 8, 9, 16, 24, 25, 27, 32, 36, 40, 49, 54, 56, 64, 81, 88, 96, 100, 104, 121, 125, 128, 135, 136, 144, 152, 160, 169, 184, 189, 196, 216, 224, 225, 232, 240, 243, 248, 250, 256, 289, 296, 297, 324, 328, 336, 343, 344, 351, 352, 360, 361, 375, 376, 384, 400, 416, 424, 441, 459 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All proper powers of any number greater than 1 (A001597(n), n>1) are a subset of this sequence. On the other hand, this is a subset of A067340 which admits also numbers k for which bigomega(k) = omega(k). In particular, prime numbers are excluded. The density of these numbers, i.e., the ratio n/a(n), apparently decreases with n, reaching 0.04420... for n = 10000000. Conjecture: n/a(n) might have a nonzero limit below 0.0427 (the density found in the interval 9500000 < n <= 10000000). LINKS Stanislav Sykora, Table of n, a(n) for n = 1..20000 Wikipedia, Arithmetic functions EXAMPLE 240 is in the sequence because 240=5^1*3^1*2^4. Hence omega(240)=3 (three distinct prime divisors) is a proper divisor of bigomega(240)=6 (six prime divisors with multiplicity). PROG (PARI) OmegaTest(n)=(bigomega(n)>omega(n))&&(bigomega(n)%omega(n)==0); Ntest(nmax, test)={my(k=1, n=0, v); v=vector(nmax); while(1, n++; if(test(n), v[k]=n; k++; if(k>nmax, break)); ); return(v); } Ntest(20000, OmegaTest) CROSSREFS Cf. A000040, A001597, A067340, A070011. Sequence in context: A280387 A243180 A100657 * A212164 A293243 A140104 Adjacent sequences:  A245077 A245078 A245079 * A245081 A245082 A245083 KEYWORD nonn AUTHOR Stanislav Sykora, Jul 11 2014 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.

Last modified December 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.)