A119711
Primes p such that p+1, p+2 and p+3 have equal number of divisors.
Original entry on oeis.org
229, 241, 373, 1831, 2053, 2503, 3109, 5861, 6053, 6151, 6871, 8293, 8821, 9161, 9829, 12049, 13591, 13781, 14293, 14887, 16087, 17737, 19141, 19333, 20389, 21493, 23333, 23509, 24151, 25771, 27109, 28807, 29269, 31337, 33413, 33941, 35509
Offset: 1
229 is OK since 230, 231 and 232 all have 8 divisors: {1,2,5,10,23,46,115,230}, {1,3,7,11,21,33,77,231} and {1,2,4,8,29,58,116,232}.
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Select[Prime@Range@5000,DivisorSigma[0,#+1]==DivisorSigma[0,#+2]==DivisorSigma[0,#+3]&]
A119705
Primes p such that the number of divisors of p+1 equals number of divisors of p+2.
Original entry on oeis.org
13, 37, 43, 97, 103, 157, 229, 241, 331, 373, 433, 541, 547, 877, 907, 1021, 1129, 1201, 1373, 1381, 1433, 1489, 1543, 1597, 1613, 1621, 1741, 1831, 1951, 1987, 2017, 2053, 2161, 2377, 2503, 2539, 2557, 2633, 2677, 2713, 2857, 2953, 3061, 3067, 3109, 3169
Offset: 1
13 is a term because 14 and 15 each have 4 divisors: {1, 2, 7, 14} and {1, 3, 5, 15}.
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Select[Range[3200], PrimeQ[#] && DivisorSigma[0, # + 1] == DivisorSigma[0, # + 2] &] (* Amiram Eldar, Jan 26 2020 *)
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isok(n) = isprime(n) && (numdiv(n+1) == numdiv(n+2)); \\ Michel Marcus, Oct 10 2013
A119728
Primes p such that p+1, p+2, p+3 and p+4 have equal number of divisors.
Original entry on oeis.org
241, 13781, 19141, 21493, 50581, 61141, 76261, 77431, 94261, 95383, 95413, 98101, 104743, 104869, 134581, 141653, 142453, 152629, 153991, 158341, 160933, 165541, 169111, 199831, 201511, 203431, 206551, 229351, 233941, 235111, 253013, 273367
Offset: 1
241 is a term since 242, 243, 244 and 245 all have 6 divisors:
{1,2,11,22,121,242},{1,3,9,27,81,243},{1,2,4,61,122,244} and {1,5,7,35,49,245}.
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Select[Prime@Range@50000,DivisorSigma[0,#+1]==DivisorSigma[0,#+2]==DivisorSigma[0,#+3]==DivisorSigma[0,#+4]&]
A119730
Primes p such that p+1, p+2, p+3, p+4 and p+5 have equal number of divisors.
Original entry on oeis.org
13781, 19141, 21493, 50581, 142453, 152629, 253013, 298693, 307253, 346501, 507781, 543061, 845381, 1079093, 1273781, 1354501, 1386901, 1492069, 1546261, 1661333, 1665061, 1841141, 2192933, 2208517, 2436341, 2453141, 2545013
Offset: 1
13781 is a term since 13782, 13783, 13784, 13785 and 13786 all have 8 divisors:
{1,2,3,6,2297,4594,6891,13782}, {1,7,11,77,179,1253,1969,13783},
{1,2,4,8,1723,3446,6892,13784}, {1,3,5,15,919,2757,4595,13785} and
{1,2,61,113,122,226,6893,13786}.
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Select[Prime@Range[1000000],DivisorSigma[0,#+1]==DivisorSigma[0,#+2]==DivisorSigma[0,#+3]==DivisorSigma[0,#+4]==DivisorSigma[0,#+5]&]
endQ[n_]:= Length[Union[DivisorSigma[0, (n + Range[5])]]]==1; Select[Prime[ Range[ 200000]],endQ] (* Harvey P. Dale, Jan 16 2019 *)
A119740
Primes p such that p+1, p+2, p+3, p+4, p+5 and p+6 have equal number of divisors.
Original entry on oeis.org
298693, 346501, 1841141, 2192933, 2861461, 3106981, 3375781, 3435589, 3437813, 3865429, 4597013, 6191461, 7016213, 7074901, 7637941, 7918373, 9196309, 10216901, 12798901, 13747429, 14100661, 14171653, 14770981, 14779189
Offset: 1
298693 is a term since 298694, 298695, 298696, 298697, 298698 and 298699 all have 8 divisors:
{1,2,11,22,13577,27154,149347,298694}, {1,3,5,15,19913,59739,99565,298695},
{1,2,4,8,37337,74674,149348,298696}, {1,7,71,497,601,4207,42671,298697},
{1,2,3,6,49783,99566,149349,298698}, {1,19,79,199,1501,3781,15721,298699}.
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Select[Prime@Range[1000000],DivisorSigma[0,#+1]==DivisorSigma[0,#+2]==DivisorSigma[0,#+3]==DivisorSigma[0,#+4]==DivisorSigma[0,#+5]==DivisorSigma[0,#+6]&]
Showing 1-5 of 5 results.
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