A128671
Least number k > 0 such that k^p does not divide the denominator of generalized harmonic number H(k,p) nor the denominator of alternating generalized harmonic number H'(k,p), where p = prime(n).
Original entry on oeis.org
20, 94556602, 444, 104, 77, 3504, 1107, 104, 2948, 903, 77, 1752, 77, 104, 370
Offset: 1
a(2) = A128673(1) = 94556602.
Cf.
A128670,
A001008,
A002805,
A058313,
A058312,
A007406,
A007407,
A119682,
A007410,
A120296,
A125581,
A126196,
A126197,
A128672,
A128673,
A128674,
A128675,
A128676.
A232067
Numbers k such that sigma(k^2) and Sum_{d|k} d*sigma(d) are both multiples of k.
Original entry on oeis.org
1, 39, 793, 2379, 7137, 76921, 230763, 692289, 2076867, 8329831, 24989493, 53695813, 74968479, 161087439, 224905437, 243762649, 324863409, 375870691, 483262317, 731287947, 1127612073, 1449786951, 2094136707, 2193863841, 2631094837, 3382836219, 3606816823
Offset: 1
-
fQ[n_] := Mod[DivisorSigma[1, n^2], n] == 0 && Mod[DivisorSum[n, #*DivisorSigma[1, #] &], n] == 0; Select[Range[100000], fQ] (* T. D. Noe, Nov 25 2013 *)
A126563
Numbers k such that the ratio of A117731(k) and A082687(k) is composite.
Original entry on oeis.org
119, 735, 5145, 36015, 252105, 1764735, 12353145
Offset: 1
-
h=0; Do[ h=h+1/(n+1)/(2n+1); f=Numerator[n*h]; g=Numerator[h]; If[ !Equal[f, g] && !PrimeQ[f/g], Print[ {n, f/g, FactorInteger[n], FactorInteger[f/g]} ] ], {n, 1, 10000} ]
-
f(n) = sum(k=1, n, 1/(n+k));
isok(k) = my(fk = f(k), q = numerator(k*fk)/numerator(fk)); (q!=1) && !isprime(q); \\ Michel Marcus, Mar 08 2023
Comments