A125135
Triangle read by rows in which row n lists prime factors of p^p - 1 where p = prime(n).
Original entry on oeis.org
3, 2, 13, 2, 2, 11, 71, 2, 3, 29, 4733, 2, 5, 15797, 1806113, 2, 2, 3, 53, 264031, 1803647, 2, 2, 2, 2, 10949, 1749233, 2699538733, 2, 3, 3, 109912203092239643840221, 2, 11, 461, 1289, 831603031789, 1920647391913
Offset: 1
Triangle begins:
3;
2, 13;
2, 2, 11, 71;
2, 3, 29, 4733;
2, 5, 15797, 1806113;
2, 2, 3, 53, 264031, 1803647;
2, 2, 2, 2, 10949, 1749233, 2699538733;
2, 3, 3, 109912203092239643840221;
2, 11, 461, 1289, 831603031789, 1920647391913;
2, 2, 7, 59, 16763, 84449, 2428577, 14111459, 58320973, 549334763;
...
n=4: p=7, 7^7-1 = 823542 = 2*3*29*4733 gives row 4.
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for p in [ n : n in [1..100] | IsPrime(n) ] do "\nDoing p =", p; n := p^p -1; Factorisation(n); end for; // John Cannon
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T:= n-> (p-> sort(map(i-> i[1]$i[2], ifactors(p^p-1)[2]))[])(ithprime(n)):
seq(T(n), n=1..10); # Alois P. Heinz, May 20 2022
A214811
Triangle read by rows: row n lists prime factors of (p^p-1)/(p-1) where p = prime(n).
Original entry on oeis.org
3, 13, 11, 71, 29, 4733, 15797, 1806113, 53, 264031, 1803647, 10949, 1749233, 2699538733, 109912203092239643840221, 461, 1289, 831603031789, 1920647391913, 59, 16763, 84449, 2428577, 14111459, 58320973, 549334763, 568972471024107865287021434301977158534824481, 149, 1999, 7993, 16651, 17317, 10192715656759, 41903425553544839998158239
Offset: 1
Triangle begins:
[3]
[13]
[11, 71]
[29, 4733]
[15797, 1806113]
[53, 264031, 1803647]
[10949, 1749233, 2699538733]
[109912203092239643840221]
[461, 1289, 831603031789, 1920647391913]
[59, 16763, 84449, 2428577, 14111459, 58320973, 549334763]
[568972471024107865287021434301977158534824481]
[149, 1999, 7993, 16651, 17317, 10192715656759, 41903425553544839998158239]
...
-
f:=proc(n) local i,t1,p,B,F;
p:=ithprime(n);
B:=(p^p-1)/(p-1);
F:=ifactors(B)[2];
lprint(n,p,B,F);
t1:=[seq(F[i][1],i=1..nops(F))];
sort(t1);
end;
A104132
Largest prime factor of pip(n)^pip(n)-1 where pip(n) is the n-th prime-indexed prime.
Original entry on oeis.org
13, 71, 1806113, 2699538733, 568972471024107865287021434301977158534824481, 5926187589691497537793497756719
Offset: 1
-
lpf[n_]:=Module[{p=Prime[Prime[n]]},FactorInteger[p^p-1][[-1,1]]]; Array[lpf,6] (* Harvey P. Dale, Nov 09 2017 *)
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piptopipm1(n) = { local(x, y); for(x=1, n, y=pip(x)^pip(x)-1; print1(bdiv(y)", "); ) }
pip(n) = { return(prime(prime(n))) }
bdiv(n) = { local(x); x=ifactor(n); return(x[length(x)]) }
ifactor(n, m=0) = { local(f, j, k, flist); flist=[]; f=Vec(factor(n, m)); for(j=1, length(f[1]), for(k = 1, f[2][j], flist = concat(flist, f[1][j]) ); ); return(flist) }
A248843
Table read by rows in which row n lists divisors of (p^p-1)/(p-1) where p = prime(n).
Original entry on oeis.org
1, 3, 1, 13, 1, 11, 71, 781, 1, 29, 4733, 137257, 1, 15797, 1806113, 28531167061, 1, 53, 264031, 1803647, 13993643, 95593291, 476218721057, 25239592216021, 1, 10949, 1749233, 2699538733, 19152352117, 29557249587617, 4722122236541789
Offset: 1
Table begins:
[1, 3],
[1, 13],
[1, 11, 71, 781],
[1, 29, 4733, 137257],
[1, 15797, 1806113, 28531167061],
[1, 53, 264031, 1803647, 13993643, 95593291, 476218721057, 25239592216021],
...
A354226
a(n) is the number of distinct prime factors of (p^p - 1)/(p - 1) where p = prime(n).
Original entry on oeis.org
1, 1, 2, 2, 2, 3, 3, 1, 4, 7, 1, 7, 5, 3, 3, 5, 3, 4, 6, 4, 10, 5, 4, 6, 6, 9, 5, 4, 5, 8, 6, 4, 11
Offset: 1
a(3)=2, since (5^5 - 1)/(5 - 1) = 11*71.
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a(n) = my(p=prime(n)); omega((p^p-1)/(p-1)); \\ Michel Marcus, May 22 2022
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from sympy import factorint, prime
def a(n): p = prime(n); return len(factorint((p**p-1)//(p-1)))
print([a(n) for n in range(1, 12)]) # Michael S. Branicky, May 23 2022
Showing 1-5 of 5 results.
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