Original entry on oeis.org
323, 899, 1763, 5249, 3239, 979801, 5459, 10763, 9179, 9701, 10403, 12319, 5646547, 24569, 19109, 19043, 22499, 50819, 41309, 32639, 46979, 34579, 39059, 125969, 49769, 49949, 154559, 48554797, 114953, 52532203, 56624063, 195499, 75077, 79799, 72899
Offset: 1
A065824(4) = 323, so a(1) = A065824[A047845(1+1)] = 323 A065824(16) = 979801 and a(6) = 979801 = A065824[A047845(1+6)]
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from math import prod
from itertools import count
from sympy import factorint, primepi
def A065884(n):
m, k = n, primepi(n+1) + n + (n+1>>1)
while m != k:
m, k = k, primepi(k) + n + (k>>1)
m = m-1>>1
for k in count(1):
f = factorint(k)
if (m+1)*k*prod((p-1)**2 for p in f)==m*prod(p**(e+2)-p for p,e in f.items()):
return k # Chai Wah Wu, Aug 12 2024
A375262
Least positive integer m such that sigma(m)/phi(m) = n + 1/2, where sigma(.) and phi(.) are given by A000203 and A000010, respectively.
Original entry on oeis.org
5, 459, 4, 10, 860, 18, 24, 11904, 588, 60, 1481172, 1080, 1320, 6236370, 1680, 144480, 10920, 674520, 27720, 25604040, 662535720, 1413720, 303783480, 4324320, 701205120
Offset: 1
a(1) = 5 with sigma(5)/phi(5) = 6/4 = 1 + 1/2.
a(2) = 459 = 3^3*17 with sigma(459)/phi(459) = 720/288 = 2 + 1/2.
a(20) = 25604040 = 2^3*3*5*7*11*17*163 with sigma(25604040)/phi(25604040) = 102021120/4976640 = 20 + 1/2.
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sigma[n_]:=sigma[n]=DivisorSigma[1,n]; phi[n_]:=phi[n]=EulerPhi[n];
tab={};Do[m=1;While[sigma[m]/phi[m]!=n+1/2,m=m+1];tab=Append[tab,m],{n,1,20}];Print[tab]
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a(n) = my(k=1); while (sigma(k)/eulerphi(k) != n + 1/2, k++); k; \\ Michel Marcus, Aug 08 2024
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from itertools import count
from math import prod
from sympy import factorint
def A375262(n):
for m in count(1):
f = factorint(m)
if ((n<<1)+1)*m*prod((p-1)**2 for p in f)==prod(p**(e+2)-p for p,e in f.items())<<1:
return m # Chai Wah Wu, Aug 11 2024
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