A243090 -id:A243090

Search: a243090 -id:a243090

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A243010

Pseudoprimes to base 5 that are not squarefree.

+10
5

4, 124, 11476, 59356, 80476, 91636, 250876, 261964, 482516, 1385836, 1926676, 2428084, 2589796, 3743476, 4101796, 6797764, 9155476, 10701076, 10743436, 11263396, 13799836, 13859956, 15570556, 20396476

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

OFFSET

1,1

COMMENTS

Any term is divisible by the square of a base 5 Wieferich prime (A123692).

Intersection of A005936 and A013929. - Michel Marcus, Aug 21 2014

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..879 (terms below 10^12)

PROG

(PARI) forcomposite(n=1, 1e9, if(Mod(5, n)^(n-1)==1, if(!issquarefree(n), print1(n, ", "))))

CROSSREFS

Cf. A005936, A123692, A158358, A243089, A243090, A244065.

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Aug 18 2014

STATUS

approved

A243089

Pseudoprimes to base 7 that are not squarefree.

+10
5

25, 325, 1825, 4525, 4825, 10225, 12025, 16725, 20425, 30025, 35425, 58825, 177025, 216525, 265525, 352225, 526825, 611425, 675925, 710425, 717025, 746425, 772525, 784225, 834025, 877825, 1125825, 1126225, 1439425, 1491025, 1579225, 1935025, 1973425, 2176525

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

OFFSET

1,1

COMMENTS

Any term is divisible by the square of a base 7 Wieferich prime (A123693).

Intersection of A005938 and A013929. - Michel Marcus, Aug 21 2014

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..3095 (terms below 10^12)

PROG

(PARI) forcomposite(n=1, 1e9, if(Mod(7, n)^(n-1)==1, if(!issquarefree(n), print1(n, ", "))))

CROSSREFS

Cf. A005938, A123693, A158358, A243010, A243090, A244065.

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Aug 18 2014

STATUS

approved

A306448

Pseudoprimes to base 9 that are not squarefree.

+10
2

4, 8, 28, 52, 121, 364, 532, 616, 1036, 1288, 3052, 3751, 4376, 4636, 4961, 5356, 6364, 7381, 8744, 11011, 11476, 12124, 15964, 19096, 19684, 21196, 21736, 24388, 26596, 29161, 31876, 32791, 37576, 40132, 45676, 47972, 53092, 61831, 67276, 72136, 80476, 80956, 86296

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

OFFSET

1,1

COMMENTS

Numbers k that are not squarefree and satisfy 9^(k-1) == 1 (mod k).

Any term is divisible by the square of a base-9 Wieferich prime ({2} U {base-3 Wieferich primes} = {2} U A014127 = {2, 11, 1006003, ...}).

Intersection of A020138 and A013929.

LINKS

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

PROG

(PARI) for(n=1, 10^5, if(Mod(9, n)^(n-1)==1 && !issquarefree(n), print1(n, ", ")))

CROSSREFS

Pseudoprimes to base b that are not squarefree: A158358 (b=2), A244065 (b=3), A243010 (b=5), A243089 (b=7), A243090 (b=8), this sequence (b=9), A306449 (b=10).

Cf. also A014127, A020138, A013929.

KEYWORD

nonn

AUTHOR

Jianing Song, Feb 16 2019

STATUS

approved

A306449

Pseudoprimes to base 10 that are not squarefree.

+10
2

9, 99, 657, 909, 1233, 11169, 13833, 19503, 20961, 23661, 51291, 69921, 90009, 99297, 109737, 139329, 203841, 237169, 256059, 321201, 339021, 346473, 460251, 475641, 686169, 760761, 927081, 1080801, 1621089, 1679931, 3100833, 3316941, 3845601, 3846051, 3942657, 4095081, 4281057

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

OFFSET

1,1

COMMENTS

Numbers k that are not squarefree and satisfy 10^(k-1) == 1 (mod k).

Any term is divisible by the square of a base-10 Wieferich prime (A045616 = {3, 487, 56598313, ...}).

Intersection of A005939 and A013929.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000

PROG

(PARI) for(n=1, 10^6, if(Mod(10, n)^(n-1)==1 && !issquarefree(n), print1(n, ", ")))

CROSSREFS

Pseudoprimes to base b that are not squarefree: A158358 (b=2), A244065 (b=3), A243010 (b=5), A243089 (b=7), A243090 (b=8), A306448 (b=9), this sequence (b=10).

Cf. also A045616, A005939, A013929.

KEYWORD

nonn

AUTHOR

Jianing Song, Feb 16 2019

STATUS

approved

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