A062959
Number of divisors of n^(n!) (A053986).
Original entry on oeis.org
1, 3, 7, 49, 121, 519841, 5041, 120961, 725761, 13168196697601, 39916801, 458885067042124801, 6227020801, 7600054456726354022401, 1710012252726814772736001, 83691159552001, 355687428096001, 81980778135594585487141085184001, 121645100408832001
Offset: 1
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a:= n-> mul(n!*i[2]+1, i=ifactors(n)[2]):
seq (a(n), n=1..20); # Alois P. Heinz, Dec 17 2011
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for(n=1,13,print(numdiv(n^(n!))))
A187751
a(n) = n^(n!) mod (n!)^n.
Original entry on oeis.org
0, 0, 0, 81, 225280, 7991790625, 1078848154238976, 65180706714634067542224001, 1650157594512930366268925848349310976, 66807065275536807794426016376688705273224158387201, 228020326859403543540241849077865865705999564800000000000000000000
Offset: 0
a(3) = 3^6 mod 6^3 = 729 mod 216 = 81.
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A187751(n):=mod(n^(n!),(n!)^n)$ makelist(A187751(n),n,0,9); /* Martin Ettl, Jan 13 2013 */
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import math
for n in range(12):
f = math.factorial(n)
print(pow(n, f, f**n))
A202336
Number of digits in n^(n!).
Original entry on oeis.org
1, 1, 1, 3, 15, 84, 561, 4260, 36413, 346276, 3628801, 41569064, 516929544, 6936548425, 99917483647, 1537944393896, 25193549397053, 437655212248536, 8036723680196724, 155554110186062367, 3165278489148945082, 67553429525569109411, 1508884070229326953381
Offset: 0
a(3) = 3 because 3^3! = 729 with 3 digits;
a(4) = 15 because 4^4! = 281474976710656 with 15 digits.
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a:= proc(n) local h;
Digits:= 1000;
1+ `if`(n=0, 0, floor(n!*simplify(log[10](n))))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Dec 17 2011
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Table[IntegerLength[n^n!],{n,0,10}] (* The program generates the first 11 terms of the sequence. *) (* Harvey P. Dale, Nov 19 2024 *)
A202358
Sum of digits of n^(n!).
Original entry on oeis.org
0, 1, 4, 18, 73, 334, 2592, 18919, 164476, 1558521, 1, 187044031, 2326111614, 31214008090
Offset: 0
a(3) = 18 because 3^3! = 729 with digit sum 7+2+9 = 18.
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ds:= proc(n) local r;
`if`(n<10, n, ds(iquo(n, 10^iquo(length(n), 2), 'r'))+ds(r))
end:
a:= n-> ds(n^n!):
seq(a(n), n=0..10); # Alois P. Heinz, Dec 17 2011
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from math import factorial
def a(n): return sum(map(int, str(n**(factorial(n)))))
print([a(n) for n in range(10)]) # Michael S. Branicky, Jan 28 2021
A213065
a(n) = n^n! - n!^n.
Original entry on oeis.org
-1, 0, 0, 513, 281474976378880, 752316384526264005099991383822237233803945956334136013765601092018187046026142190625
Offset: 0
A307031
n to the power n double factorial, n^(n!!).
Original entry on oeis.org
1, 4, 27, 65536, 30517578125, 22452257707354557240087211123792674816, 54361846697263307560529495055267343940077014163990039113495978834700158362117849904436807
Offset: 1
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Table[n^n!!,{n,7}] (* Harvey P. Dale, Aug 11 2021 *)
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def doublefactorial(n):
if n <= 0:
return 1
else:
return n * doublefactorial(n-2)
for n in range(1,m):
print(n**doublefactorial(n))
Showing 1-6 of 6 results.
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