A080569
a(n) is the first number in the first run of at least n successive numbers, all having exactly 3 distinct prime factors.
Original entry on oeis.org
30, 230, 644, 1308, 2664, 6850, 10280, 39693, 44360, 48919, 218972, 526095, 526095, 526095, 17233173, 127890362, 29138958036, 146216247221, 23671413563491, 36966736685739
Offset: 1
a(3) = 644 because 644 = 2^2 * 7 * 23, so omega(644) = 3, 645 = 3*5*43, so omega(645) = 3 and 646 = 2*17*19, so omega(646) = 3 and no other number n < 644 has omega(n)=omega(n+1)=omega(n+2)=3.
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k = 1; Do[ While[ Union[ Table[ Length[ FactorInteger[i]], {i, k, k + n - 1}]] != {3}, k++ ]; Print[k], {n, 1, 16}]
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k=1; for(i=1,600000,s=1; for(j=1,k,if(omega(i+j-1)!=3,s=0,)); if(s==1,print1(i,", "); k++; i--,) )
A359636
a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have at least n distinct prime factors.
Original entry on oeis.org
7, 19, 643, 51427, 8083633, 1077940147, 75582271489, 34710483181813
Offset: 1
a(1) = 7: trivially, the 3 composites 8 = 2^3, 9 = 3^2, 10 = 2*5, have at least one distinct prime factor;
a(2) = 19: 20 = 2^2*5, 21 = 3*7, 22 = 2*11 all have 2 distinct prime factors;
a(3) = 643: 644 = 2^2*7*23, 645 = 3*5*43, 646 = 2*17*19, 647 is prime.
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a359636(maxp) = {my (k=1, pp=3); forprime (p=5, maxp, my(mi=oo); if (p-pp>2, for (j=pp+1, p-1, my(mo=omega(j)); if (mo=k, print1(pp,", "); k++)); pp=p)};
a359636(10^7)
A185042
Initial term of first run of exactly n consecutive numbers with 4 distinct prime factors.
Original entry on oeis.org
210, 7314, 37960, 134043, 357642, 2713332, 1217250, 14273478, 44939642, 76067298, 163459742, 547163235, 2081479430, 2771263512, 11715712410, 17911205580, 56608713884, 203594236366, 118968284928, 2500769994070, 3157129230489, 22498525938216, 585927201062
Offset: 1
a(6) > a(7) because the first run of 6 consecutive integers i with A001221(i)=4 is not maximal.
A384507
Initial term of first run of exactly n consecutive numbers with exactly 5 distinct prime factors.
Original entry on oeis.org
2310, 254540, 1042404, 21871365, 129963314, 830692265, 4617927894, 18297409143, 41268813542, 287980277114, 1182325618032, 6455097761454, 14207465691240, 54049709480208, 90987640183352, 1164838922284960, 546525829796442
Offset: 1
a(16) > a(17) because the first run of 16 consecutive integers i with A001221(i)=5 is not a maximal run.
Showing 1-4 of 4 results.
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