A215015
Number of sphenic twins up to 10^n.
Original entry on oeis.org
0, 0, 11, 337, 4206, 43330, 417479, 3917508, 36358375, 336046778, 3105465308, 28739218426
Offset: 1
a(3) = 11 since there are 11 sphenic twins below 10^3 whose smaller members are 230, 285, 429, 434, 609, 645, 741, 805, 902, 969, 986.
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sphQ[n_]:= FactorInteger[n][[;;,2]] == {1, 1, 1}; c = 0; p = 10; q1 = 0; seq = {}; Do[q2 = sphQ[k]; If[q1 && q2, c++]; If[k == p, AppendTo[seq, c]; p*=10]; q1 = q2, {k, 2, 10^5}]; seq (* Amiram Eldar, Dec 26 2019 *)
A359642
Number of numbers <= 10^n that are products of 4 distinct primes.
Original entry on oeis.org
0, 0, 16, 429, 7039, 92966, 1103888, 12364826, 133702610, 1413227318, 14709861824, 151469044739, 1547593008310, 15721130285808, 159006397271949, 1602820838558101, 16114386617828822, 161673560523193369, 1619352576852638084, 16197963371445222701
Offset: 1
a(3) = 16 = #{210, 330, 390, 462, 510, 546, 570, 690, 714, 770, 798, 858, 870, 910, 930, 966}
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a(n) = my(N=10^n); (f(m, p, k, j=1)=my(s=sqrtnint(N\m, k), count=0); if(k==2, forprime(q=p, s, count += primepi(N\(m*q)) - j; j+=1); return(count)); forprime(q=p, s, count += f(m*q, q+1, k-1, j+1); j+=1); count); f(1, 2, 4); \\ Daniel Suteu, Jan 11 2023
A215152
Number of sphenic triples up to 10^n.
Original entry on oeis.org
0, 0, 0, 21, 445, 5457, 55576, 527138, 4824694, 43484124, 389855718
Offset: 1
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issemiprime(n) = factor(n)[,2]~ == [1,1];
issphenic(n) = factor(n)[,2]~ == [1,1,1];
list(nmax) = {my(c = 0, pow = 10, lim = 10^nmax/2+1); forstep(k = 1, lim, 2, if(issemiprime(k) && issphenic(2*k-1) && issphenic(2*k+1), c++); if(2*k-1 > pow, print1(c, ", "); pow *= 10));} \\ Amiram Eldar, Jan 15 2025
A359644
Number of numbers <= 10^n that are products of 5 distinct primes.
Original entry on oeis.org
0, 0, 0, 24, 910, 18387, 286758, 3884936, 48396263, 571221133, 6499261245, 72047682376, 783561421371, 8399470576016, 89038389261794, 935562667202846, 9761003371437806, 101253973351371824, 1045354835981786609
Offset: 1
a(4) = 24 = #{2310, 2730, 3570, 3990, 4290, 4830, 5610, 6006, 6090, 6270, 6510, 6630, 7410, 7590, 7770, 7854, 8610, 8778, 8970, 9030, 9282, 9570, 9690, 9870}
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a(n) = my(N=10^n); (f(m,p,k,j=1)=my(s=sqrtnint(N\m, k), count=0); if(k==2, forprime(q=p, s, count += primepi(N\(m*q)) - j; j+=1); return(count)); forprime(q=p, s, count += f(m*q, q+1, k-1, j+1); j+=1); count); f(1, 2, 5); \\ Daniel Suteu, Jan 10 2023
A379570
Number of n-digit numbers that have exactly 8 divisors.
Original entry on oeis.org
0, 10, 170, 1934, 20067, 202246, 2003991, 19674052, 192215670, 1873532828, 18242642732, 177582019015, 1728951136938, 16840198807124, 164117159854744, 1600427660469575, 15617400806292160
Offset: 1
A359645
Number of numbers <= 10^n that are products of 6 distinct primes.
Original entry on oeis.org
0, 0, 0, 0, 20, 1235, 32396, 605939, 9446284, 131733664, 1706815354, 21008871506, 249145286508, 2873325692759, 32433194803107, 359960491516138, 3941261642520039, 42679704453671033, 457980431402674541
Offset: 1
a(5) = 20 = #{30030, 39270, 43890, 46410, 51870, 53130, 62790, 66990, 67830, 71610, 72930, 79170, 81510, 82110, 84630, 85470, 91770, 94710, 98670, 99330}.
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a(n) = my(N=10^n); (f(m, p, k, j=1)=my(s=sqrtnint(N\m, k), count=0); if(k==2, forprime(q=p, s, count += primepi(N\(m*q)) - j; j+=1); return(count)); forprime(q=p, s, count += f(m*q, q+1, k-1, j+1); j+=1); count); f(1, 2, 6); \\ Daniel Suteu, Jan 11 2023
Showing 1-6 of 6 results.
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