Original entry on oeis.org
1, 4, 20, 20, 714, 714, 25550, 90180, 142803, 809300
Offset: 1
A045983
Numbers k such that n or more consecutive integers starting at k have the same number of distinct prime divisors.
Original entry on oeis.org
1, 2, 2, 2, 54, 91, 141, 141, 44360, 48919, 218972, 526095, 526095, 526095, 17233173, 127890362, 29138958036, 118968284928, 118968284928, 585927201062, 585927201062, 585927201062, 585927201062, 313978488186061, 453918847597184, 453918847597184, 455626105596320
Offset: 1
a(5) = 54 as 54, 55, 56, 57, 58 all have 2 prime divisors.
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v=vector(16); n=0; c1=0; for(k=1, 127890377, c2=omega(k); if(c1==c2, n++; if(v[n]==0, v[n]=k-n+1; print(n " " v[n])), n=1; c1=c2)) /* Donovan Johnson, Mar 29 2013 */
A075028
a(1) = 1, then a(n) = the smallest number k such that the number of divisors of the n numbers from k through k+n-1 are in strictly ascending order.
Original entry on oeis.org
1, 1, 61, 61, 11371, 11371, 7392171, 168776043, 1584614377, 38045133481, 30386250649371, 1848289766450821
Offset: 1
a(3) = 61 = a(4) as tau(61) = 2 < tau(62) = 4 < tau(63) = 6 < tau(64) = 7.
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003
A075029
a(n) is the smallest number k such that the number of divisors of the n numbers from k through k+n-1 are decreasing.
Original entry on oeis.org
1, 4, 45, 80, 28974, 28974, 8489103, 80314575, 5196065775, 77506573550, 166622964149389, 489289301397948
Offset: 1
a(4) = 80, as tau(80) = 10 > tau(81) = 5 > tau(82) = 4 > tau(83) = 2, and no smaller sequence of 4 consecutive integers satisfies such a chain of inequalities.
- J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 45, p. 17, Ellipses, Paris 2008.
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n=2; for(k=1, 100, while(1, m=n; s=1; while(numdiv(m)=k, print1(n-1, ", "); break); n=n+1))
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apply( {A075029(n)=for(k=4^(n-1),oo, my(d=numdiv(k)); d(d=numdiv(k+j)) || [k+=j-1, next(2)]); return(k))}, [1..6]) \\ For illustration - becomes slow for n >= 7. - M. F. Hasler, May 26 2025
A075046
a(n) = the smallest number k such that the number of divisors of the n numbers from k through k+n-1 are in nondescending order.
Original entry on oeis.org
1, 1, 1, 1, 241, 241, 12853, 12853, 234613, 376741, 78312721, 125938261, 4019167441, 16586155153, 35237422882, 1296230533473, 42301168491121, 61118966262061
Offset: 1
a(5) = 241 = a(6) as tau(241) = 2 < tau(242) = tau(243) = tau(244) = tau(245) = 6 < tau(246).
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k = 1; Do[ While[t = Table[ DivisorSigma[0, i], {i, k, k + n - 1}]; t != Sort[t], k++ ]; Print[k], {n, 1, 11}]
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003
Showing 1-5 of 5 results.
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