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
A218448
First of a run of 5 consecutive numbers with same prime signature.
Original entry on oeis.org
204323, 3252571, 5205074, 7201674, 20182921, 28387953, 36193650, 43216722, 51049537, 56155074, 57070850, 61961315, 62167075, 65425473, 76647074, 82507473, 92658049, 95943321, 100498849, 107236449, 109751473, 110899321, 112198075, 112477849, 116736323
Offset: 1
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is_A218448(n)={my(f);!for(i=0,4,f!=(f=vecsort(factor(n+i)[,2])) & i & return)}
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f(k)=vecsort(factor(k)[,2]~,,4)
t=f(n=2);while(n<1e8, for(i=n+1, n+4, tt=f(i); if(tt!=t, n=i; t=tt; next(2))); print1(n", "); n++) \\ Charles R Greathouse IV, Oct 28 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)}
A359746
Numbers k such that k, k+1 and k+2 have the same ordered prime signature.
Original entry on oeis.org
33, 85, 93, 141, 201, 213, 217, 301, 393, 445, 633, 697, 921, 1041, 1137, 1261, 1309, 1345, 1401, 1641, 1761, 1837, 1885, 1893, 1941, 1981, 2013, 2101, 2181, 2217, 2305, 2361, 2433, 2461, 2517, 2641, 2665, 2721, 2733, 3097, 3385, 3601, 3693, 3729, 3865, 3901, 3957
Offset: 1
33 is a term since 33 = 3^1 * 11^1, 34 = 2^1 * 17^1, and 35 = 5^1 * 7^1 have the same ordered prime signature, (1, 1).
4923 is a term since 4923 = 3^2 * 547^1, 4924 = 2^2 * 1231^1, and 4925 = 5^2 * 197^1 have the same ordered prime signature, (2, 1).
603 is a term of A052214 but not a term of this sequence, since 603 = 3^2 * 67^1, 604 = 2^2 * 151^1, and 605 = 5^1 * 11^2 have different ordered prime signatures, (2, 1) or (1, 2).
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q[n_] := SameQ @@ (FactorInteger[#][[;; , 2]]& /@ (n + {0, 1, 2})); Select[Range[2, 4000], q]
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lista(nmax) = {my(e1 = [], e2 = factor(2)[,2]); for(n = 3, nmax, e3 = factor(n)[,2]; if(e1 == e2 && e2 == e3, print1(n-2, ", ")); e1 = e2; e2 = e3); }
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 1-5 of 5 results.
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