A136371
Numbers k such that A136370(k) is prime.
Original entry on oeis.org
1, 2, 3, 5, 46, 227, 232, 336, 360, 3919
Offset: 1
Cf.
A024530: numerator of Sum_{k=1..n} (-1)^k/prime(k).
Cf.
A136368: numerator of Sum_{k=1..n} (-1)^(k+1)/prime(k)^2.
Cf.
A136370: numerator of 1 - Sum_{k=1..n} (-1)^(k+1)/prime(k)^2.
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f=1; Do[ p=Prime[n]; f=f - (-1)^(n+1)*1/p^2; g=Numerator[f] ;If[ PrimeQ[g], Print[ {n, g} ] ], {n, 1, 100} ]
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# uses A136370gen() and imports from A136370
from sympy import isprime
def agen(): yield from (k for k, ak in enumerate(A136370gen(), 1) if isprime(ak))
print(list(islice(agen(), 5))) # Michael S. Branicky, Jun 26 2022
A061742
a(n) is the square of the product of first n primes.
Original entry on oeis.org
1, 4, 36, 900, 44100, 5336100, 901800900, 260620460100, 94083986096100, 49770428644836900, 41856930490307832900, 40224510201185827416900, 55067354465423397733736100, 92568222856376731590410384100, 171158644061440576710668800200900
Offset: 0
a(4) = 2^2 * 3^2 * 5^2 * 7^2 = 44100.
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[n eq 0 select 1 else (&*[NthPrime(j)^2: j in [1..n]]): n in [0..20]]; // G. C. Greubel, Apr 19 2019
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a:= proc(n) option remember; `if`(n=0, 1, ithprime(n)^2*a(n-1)) end:
seq(a(n), n=0..15); # Alois P. Heinz, May 14 2020
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a[n_]:=Product[Prime[i]^2, {i, 1, n}]; (* Vladimir Joseph Stephan Orlovsky, Dec 05 2008 *)
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for(n=0,20,print1(prod(k=1,n, prime(k)^2), ", "))
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{ n=-1; m=1; forprime (p=2, prime(101), write("b061742.txt", n++, " ", m^2); m*=p ) } \\ Harry J. Smith, Jul 27 2009
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[product(nth_prime(j)^2 for j in (1..n)) for n in (0..20)] # G. C. Greubel, Apr 19 2019
A136365
Numbers k such that A075986(k) is prime.
Original entry on oeis.org
1, 171, 210, 550, 1445, 1809, 2176, 2719
Offset: 1
Cf.
A075986 (numerator of 1 + 1/p(1)^2 + ... + 1/p(n)^2, where p(k) = prime(k)).
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f=1; Do[ p=Prime[n]; f=f + 1/p^2; g=Numerator[ f ]; If[ PrimeQ[ g ], Print[ {n, g} ] ], {n, 1, 210} ]
A136366
Numbers k such that A024530(k) is prime.
Original entry on oeis.org
3, 4, 5, 10, 21, 31, 55, 77, 121, 135, 148, 192, 425, 570, 612, 649, 1293, 2326, 3646
Offset: 1
Cf.
A024530 (numerator of Sum_{k=1..n} (-1)^k / prime(k)).
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f=0; Do[ p=Prime[n]; f=f + (-1)^(n+1)*1/p; g=Numerator[f] ;If[ PrimeQ[g], Print[ {n, g} ] ], {n, 1, 150} ]
A136368
Numerator of Sum_{k=1..n} (-1)^(k+1)/prime(k)^2.
Original entry on oeis.org
1, 5, 161, 6989, 889769, 145034861, 42816875729, 15196271678069, 8132911703794601, 6790008314246422541, 6567054920481119894801, 8950073675937467308565669, 15100141203716305943432625689
Offset: 1
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[Numerator(&+[(-1)^(k+1)/NthPrime(k)^2:k in [1..n]]): n in [1..13]]; // Marius A. Burtea, Aug 26 2019
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Table[Numerator[Sum[(-1)^(k+1)/Prime[k]^2, {k, 1, n}]], {n, 1, 20}]
A136369
Numbers k such that A136368(k) is prime.
Original entry on oeis.org
2, 5, 6, 8, 18, 20, 98, 1863
Offset: 1
Cf.
A024530 (numerator of Sum_{k=1..n} (-1)^k / prime(k)).
Cf.
A136368 (numerator of Sum_{k=1..n} (-1)^(k+1)/prime(k)^2).
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f=0; Do[ p=Prime[n]; f=f + (-1)^(n+1)*1/p^2; g=Numerator[f] ;If[ PrimeQ[g], Print[ {n, g} ] ], {n, 1, 100} ]
A136367
Numbers k such that A024529(k+1) is prime.
Original entry on oeis.org
2, 3, 4, 5, 11, 59, 397, 613, 906, 1560, 2162, 2915, 5211
Offset: 1
Cf.
A024529: numerator of 1 + Sum_{k=1..n-1} (-1)^k/prime(k).
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f=1; Do[ p=Prime[n]; f=f + (-1)^n*1/p; g=Numerator[f] ;If[ PrimeQ[g], Print[ {n, g} ] ], {n, 1, 60} ]
Showing 1-7 of 7 results.
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