A246852
Numbers n such that sigma(n+2) - sigma(n) = n + 2.
Original entry on oeis.org
1, 2, 22, 14926, 31048, 69106, 246262, 5860168, 307164670, 881198662, 1489455646, 2386555630, 8225563702, 14311679062, 111494234182, 154357775302, 299004519622, 870455062822, 970388922262, 991817878342, 1677028870822, 1782783762502, 1830446935222
Offset: 1
Number 22 is in sequence because sigma(22+2) - sigma(22) = 60 - 36 = 24 = 22 + 2.
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[n:n in[1..10^7] | SumOfDivisors(n+2)-SumOfDivisors(n) eq n+2]
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Select[Range[6*10^6], DivisorSigma[1, # + 2] - DivisorSigma[1, #] == # + 2 &] (* Jake L Lande, Jun 30 2024 *)
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for(n=1,10^7,if(sigma(n+2)-sigma(n)==n+2,print1(n,", "))) \\ Derek Orr, Sep 05 2014
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, ...
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
Showing 1-4 of 4 results.
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