A352970 -id:A352970

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A354609

Carmichael numbers ending in 1.

+10
5

561, 2821, 6601, 8911, 15841, 29341, 41041, 75361, 101101, 115921, 162401, 172081, 188461, 252601, 314821, 340561, 399001, 410041, 488881, 512461, 530881, 552721, 656601, 658801, 838201, 852841, 1024651, 1152271, 1193221, 1461241, 1615681, 1857241, 1909001, 2100901, 2113921, 2433601, 2455921, 2704801, 3057601

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to Carmichael numbers

MATHEMATICA

Select[10*Range[0, 3*10^5] + 1, CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] &] (* Amiram Eldar, Jul 08 2022 *)

PROG

(Python)

from itertools import islice

from sympy import nextprime, factorint

def A354609_gen(): # generator of terms

p, q = 3, 5

while True:

for n in range(p+2+(-p-1)%10, q, 10):

f = factorint(n)

if max(f.values()) == 1 and not any((n-1) % (p-1) for p in f):

yield n

p, q = q, nextprime(q)

A354609_list = list(islice(A354609_gen(), 30)) # Chai Wah Wu, Jul 24 2022

CROSSREFS

Intersection of A002997 and A017281.

Cf. A352970, A355305, A355307, A355309.

KEYWORD

nonn,base

AUTHOR

Omar E. Pol, Jul 08 2022

STATUS

approved

A355305

Carmichael numbers ending in 5.

+10
5

1105, 2465, 10585, 62745, 278545, 449065, 825265, 1050985, 2531845, 3224065, 3664585, 5632705, 6054985, 9582145, 11119105, 12945745, 13187665, 13992265, 15403285, 21584305, 22665505, 28787185, 31692805, 36121345, 37354465, 39353665, 40280065, 41298985, 47006785, 60112885, 67371265, 74165065, 84417985

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to Carmichael numbers

MATHEMATICA

Select[10*Range[0, 10^7] + 5, CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] &] (* Amiram Eldar, Jul 07 2022 *)

PROG

(PARI) Korselt(n) = my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1;

isok(n) = ((n%10)==5) && !isprime(n) && Korselt(n) && n>1; \\ Michel Marcus, Jul 07 2022; after A002997

(Python)

from itertools import islice

from sympy import factorint, nextprime

def A355305_gen(): # generator of terms

p, q = 3, 5

while True:

for n in range(p+2+(-p+3)%10, q, 10):

f = factorint(n)

if max(f.values()) == 1 and not any((n-1) % (p-1) for p in f):

yield n

p, q = q, nextprime(q)

A355305_list = list(islice(A355305_gen(), 10)) # Chai Wah Wu, Jul 24 2022

CROSSREFS

Intersection of A002997 and A017329.

Cf. A352970, A354609, A355307, A355309.

KEYWORD

nonn,base

AUTHOR

Omar E. Pol, Jul 03 2022

STATUS

approved

A355307

Carmichael numbers ending in 7.

+10
5

46657, 126217, 748657, 1569457, 4909177, 9613297, 11972017, 40160737, 55462177, 65037817, 106041937, 161035057, 178451857, 193910977, 196358977, 311388337, 328573477, 338740417, 358940737, 403043257, 461502097, 499310197, 556450777, 569332177, 633639097, 784966297, 902645857, 981789337, 1125038377

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to Carmichael numbers

MATHEMATICA

Select[10*Range[0, 10^7] + 7, CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] &] (* Amiram Eldar, Jul 24 2022 *)

PROG

(Python)

from itertools import count, islice

from sympy import factorint

def A355307_gen(): # generator of terms

for n in count(7, 10):

f = factorint(n)

if len(f) == sum(f.values()) > 1 and not any((n-1) % (p-1) for p in f):

yield n

A355307_list = list(islice(A355307_gen(), 5)) # Chai Wah Wu, Jul 25 2022

CROSSREFS

Intersection of A002997 and A017353.

Cf. A352970, A354609, A355305, A355309.

KEYWORD

nonn,base

AUTHOR

Omar E. Pol, Jul 24 2022

STATUS

approved

A355309

Carmichael numbers ending in 3.

+10
5

52633, 63973, 334153, 670033, 997633, 2508013, 2628073, 5968873, 6733693, 13696033, 15829633, 15888313, 18900973, 26280073, 27336673, 46483633, 53711113, 65241793, 67653433, 75765313, 124630273, 133344793, 158864833, 182356993, 227752993, 242641153, 292244833, 426821473, 577240273, 580565233, 600892993

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to Carmichael numbers

MATHEMATICA

Select[10*Range[0, 10^7] + 3, CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] &] (* Amiram Eldar, Jul 25 2022 *)

PROG

(Python)

from itertools import count, islice

from sympy import factorint

def A355309_gen(): # generator of terms

for n in count(3, 10):

f = factorint(n)

if len(f) == sum(f.values()) > 1 and not any((n-1) % (p-1) for p in f):

yield n

A355309_list = list(islice(A355309_gen(), 5)) # Chai Wah Wu, Jul 26 2022

CROSSREFS

Intersection of A002997 and A017305.

Cf. A352970, A354609, A355305, A355307.

KEYWORD

nonn,base

AUTHOR

Omar E. Pol, Jul 25 2022

STATUS

approved

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