A034173
a(n) is minimal such that prime factorizations of a(n), ..., a(n)+n-1 have same exponents.
Original entry on oeis.org
1, 2, 33, 19940, 204323, 380480345, 440738966073
Offset: 1
a(4) = 19940 because 19940, ..., 19943 all have the form p^2 q r.
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A034173(n)={my(f);for(k=1,oo,f=0;for(i=1,n, f==(f=vecsort(factor(k+n-i)[,2])) || i==1 || [k+=n-i; next(2)]);return(k))} \\ M. F. Hasler, Oct 23 2012
A175590
Numbers k with prime signature(k) = prime signature(k+1) = prime signature(k+2) = prime signature(k+3).
Original entry on oeis.org
19940, 49147, 54585, 118923, 136825, 183554, 204323, 204324, 262932, 304675, 361275, 361322, 476377, 486962, 506905, 619722, 668211, 734948, 854018, 937025, 938203, 999649, 1062025, 1118275, 1335572, 1336075, 1356324, 1466225, 1541491
Offset: 1
a(1) = 2^2 * 5 * 997; a(1)+1 = 3 * 17^2 * 23; a(1)+2 = 2 * 13^2 * 59; a(1)+3 = 7^2 * 11 * 37. All have prime signature {2, 1, 1}.
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SequencePosition[Table[Sort[FactorInteger[n][[All,2]]],{n,1542000}],{x_,x_,x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* The program will take a long time to run. *) (* Harvey P. Dale, Jun 09 2021 *)
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sig(n)={vecsort(factor(n)[,2])}; s=sig(1);for(n=1,1e6,t=sig(n+1);if(s==t&t==sig(n+2)&t==sig(n+3),print1(n-1,","));s=t)
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is_A175590(n)={my(f(n)=vecsort(factor(n)[,2]),t=f(n));!for(i=1,3,f(n+i)!=t & return)} \\ M. F. Hasler, Nov 01 2012
A218455
First of a run of 6 consecutive numbers with same prime signature.
Original entry on oeis.org
380480345, 2713001274, 6282718946, 7209536449, 9809067073, 10684724346, 12008728850, 14824913049, 17231547073, 17552118546, 17659180314, 18036555273, 20473171322, 21507097001, 23676804346, 24742649321, 25401767522, 25694056449, 27656894273, 28259097818
Offset: 1
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is_A218455(n)={my(s(n)=vecsort(factor(n)[,2]),t=s(n));!for(m=n+1,n+5, t!=s(m) & return)}
A218865
First of a run of 7 consecutive numbers with same prime signature.
Original entry on oeis.org
440738966073, 464881210073, 645462662449, 914549532721, 932537185321, 936083045673, 1043710445721, 1091100709673, 1225660528209, 1349165568945, 1602377996921, 1682159750473, 1714275593649, 1730241245545, 1756186304521, 1872671302049, 1956516794721, 1987087485225
Offset: 1
The 7 consecutive numbers from 645462662449 to 645462662455 all have a prime signature of 2,1,1,1.
Showing 1-4 of 4 results.
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