A246851
a(n) = smallest number k such that sigma(k+n) - sigma(k) = k + n, or -1 if no solution exists.
Original entry on oeis.org
1, 1, 7, 1, 3577, 1, 25, 8, 13, 1, 403668223, 1, 833, 262, 19, 1, 27, 1, 793, 5, 45, 1, 1795, 66, 8, 9, 31, 1, 2005, 1, 309, 32, 261, 4238, 22490141, 1, 21, 40, 43, 1, 399, 1, 1897, 262, 193, 1, 27, 1252907952, 711, 49, 1158765, 1, 271259, 27, 129, 20518072
Offset: 1
Sequence of numbers k < 10^7 such that sigma(k+n) - sigma(k) = k + n for 1 <= n <= 10:
n = 1: 1, 5, 8585, 16119, ... (A067816).
n = 2: 1, 2, 22, 14926, 31048, 69106, 246262, 5860168, ... (A246852).
n = 3: 7, 6285, 4693485, ... (A246853).
n = 4: 1, 4, 26, 122, 146, 458, 746, 3746, 47612, ... (A246854).
n = 5: 3577, 14773, 2843579, ... (A246855).
n = 6: 1, 3, 114, 116058, 340014, ...
n = 7: 25, 65017, ...
n = 8: 8, 34, 76, 13474, 19042, ...
n = 9: 13, 1743, 1773, 4323, 53175, 109035, 138535, ...
n = 10: 1, 20, 1958, 35150, 49010, 246686, 1030046, 1240694, ...
A246853
Numbers n such that sigma(n+3) - sigma(n) = n + 3.
Original entry on oeis.org
7, 6285, 4693485, 54028959, 75898473, 724416741, 2359059709, 4901493769, 321212249593, 511578306649, 534245763769, 6158645822473
Offset: 1
Number 7 is in sequence because sigma(7+3) - sigma(7) = 18 - 8 = 10 = 7 + 3.
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[n:n in[1..10^7] | SumOfDivisors(n+3)-SumOfDivisors(n) eq n+3]
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for(n=1,10^7,if(sigma(n+3)-sigma(n)==n+3,print1(n,", "))) \\ Derek Orr, Sep 05 2014
A246854
Numbers n such that sigma(n+4) - sigma(n) = n + 4.
Original entry on oeis.org
1, 4, 26, 122, 146, 458, 746, 3746, 47612, 16065500, 388978292, 5313509288, 64278616556
Offset: 1
Number 26 is in sequence because sigma(26+4) - sigma(26) = 72 - 42 = 30 = 26 + 4.
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[n:n in[1..10^7] | SumOfDivisors(n+4)-SumOfDivisors(n) eq n+4]
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for(n=1,10^7,if(sigma(n+4)-sigma(n)==n+4,print1(n,", "))) \\ Derek Orr, Sep 05 2014
A246855
Numbers k such that sigma(k+5) - sigma(k) = k + 5.
Original entry on oeis.org
3577, 14773, 2843579
Offset: 1
Number 3577 is in sequence because sigma(3577+5) - sigma(3577) = 7800 - 4218 = 3582 = 3577 + 5.
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[n:n in[1..10^7] | SumOfDivisors(n+5)-SumOfDivisors(n) eq n+5];
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Select[Range[285*10^4],DivisorSigma[1,#+5]-DivisorSigma[1,#]==#+5&] (* Harvey P. Dale, Jun 21 2024 *)
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for(n=1,10^7,if(sigma(n+5)-sigma(n)==n+5,print1(n,", "))) \\ Derek Orr, Sep 05 2014
A260420
Numbers n such that sigma(n+1) - sigma(n-1) = n+1.
Original entry on oeis.org
2, 3, 23, 14927, 31049, 69107, 246263, 5860169, 307164671, 881198663, 1489455647, 2386555631, 8225563703, 14311679063, 111494234183, 154357775303, 299004519623, 870455062823, 970388922263, 991817878343, 1677028870823, 1782783762503, 1830446935223
Offset: 1
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[n: n in [2..5*10^6] | DivisorSigma(1, n+1) - DivisorSigma(1, n-1) eq n+1]; // Vincenzo Librandi, Jul 26 2015
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Select[Range@ 1000000, DivisorSigma[1, # + 1] - DivisorSigma[1, # - 1] == # + 1 &] (* Michael De Vlieger, Jul 25 2015 *)
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for(n=2,1e9,sigma(n+1)-sigma(n-1)==n+1&&print1(n","))
A260071
Primes p such that sigma(p) = sigma(p+1) - sigma(p-1).
Original entry on oeis.org
2, 3, 23, 970388922263, 991817878343, 1677028870823
Offset: 1
23 is in the sequence because sigma(24) - sigma(22) = 60 - 36 = 24 = sigma(23).
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[n: n in [1..1000000] | IsPrime(n) and SumOfDivisors(n) eq ((SumOfDivisors(n+1)) - (SumOfDivisors(n-1)))];
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[n: n in [A076530(n)] | IsPrime(n)];
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is_ok(index)=my(p=prime(index)); p+1==sigma(p+1)-sigma(p-1);
main(size)=my(v=vector(size),index=1);for(i=1,size,while(!is_ok(index),index++);v[i]=prime(index);index++); v \\ Anders Hellström, Jul 14 2015
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has(p)=p+1==sigma(p+1)-sigma(p-1)
select(has, primes(1000)) \\ Charles R Greathouse IV, Jul 22 2015
Showing 1-6 of 6 results.
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