A125238 -id:A125238 - cp's OEIS frontend

A317044 Numbers k such that A(k+1) = A(k) + 1, where A() = A005100() are the deficient numbers.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 17, 18, 20, 21, 24, 25, 26, 27, 29, 30, 33, 34, 35, 36, 38, 39, 40, 41, 44, 45, 47, 48, 49, 50, 52, 53, 56, 57, 58, 59, 62, 63, 65, 66, 69, 70, 71, 72, 74, 75, 79, 80, 82, 83, 86, 87, 88, 89, 91, 92, 93, 94, 96, 97, 98

Offset: 1

Muniru A Asiru, Aug 04 2018

nonn

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

A317047 is the main sequence for this entry.
Numbers k such that A(k+1) = A(k) + j, where A() = A005100() are the deficient numbers: this sequence (j=1), A317045 (j=2), A317046 (j=3).
Cf. A005100, A125238.

A:=Filtered([1..150],k->Sigma(k)<2*k);;  a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+1);

with(numtheory): A:=select(k->sigma(k)<2*k,[$1..150]):
  a:=select(j->A[j+1]=A[j]+1,[$1..nops(A)-1]);

Position[Differences[Select[Range[130], DivisorSigma[1, #] < 2*# &]], 1] // Flatten (* Amiram Eldar, Mar 15 2024 *)

Sequence is { k | A005100(k+1) = A005101(k) + 1 }.

Sequence is { k | A125238(k) = 1 }.

A317045 Numbers k such that A(k+1) = A(k) + 2, where A() = A005100() are the deficient numbers.

Original entry on oeis.org

5, 10, 15, 16, 19, 22, 23, 28, 31, 32, 37, 42, 43, 46, 51, 54, 55, 60, 61, 64, 67, 68, 73, 76, 77, 78, 81, 84, 85, 90, 95, 100, 105, 106, 109, 114, 119, 122, 123, 128, 133, 134, 137, 142, 147, 150, 151, 152, 155, 158, 159, 164, 167, 168, 169, 172, 177, 182

Offset: 1

Muniru A Asiru, Aug 04 2018

nonn

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

A317048 is the main sequence for this entry.
Numbers k such that A(k+1) = A(k) + j, where A() = A005100() are the deficient numbers: A317044 (j=1), this sequence (j=2), A317046 (k=3).
Cf. A005100, A125238.

A:=Filtered([1..300],k->Sigma(k)<2*k);;  a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+2);

with(numtheory): A:=select(k->sigma(k)<2*k,[$1..300]):
 a:=select(j->A[j+1]=A[j]+2,[$1..nops(A)-1]);

Position[Differences[Select[Range[250], DivisorSigma[1, #] < 2*# &]], 2] // Flatten (* Amiram Eldar, Mar 15 2024 *)

Sequence is { k | A005100(k+1) = A005101(k) + 2 }.

Sequence is { k | A125238(k) = 2 }.

A317046 Numbers k such that A(k+1) = A(k) + 3, where A() = A005100() are the deficient numbers.

Original entry on oeis.org

4340, 4494, 5572, 8278, 16351, 16506, 19666, 20614, 29619, 32386, 37349, 42805, 44134, 46183, 52345, 53222, 57553, 58033, 59930, 60966, 61412, 61657, 63553, 63643, 67509, 68925, 73829, 77801, 78888, 80309, 82269, 84099, 87737, 87892, 90270, 91697, 91966

Offset: 1

Muniru A Asiru, Aug 04 2018

nonn

Muniru A Asiru, Table of n, a(n) for n = 1..10000

A317049 is the main sequence for this entry.
Numbers k such that A(k+1) = A(k) + j, where A() = A005100() are the deficient numbers: A317044 (j=1), A317045 (j=2), this sequence (j=3).
Cf. A005100, A125238.

A:=Filtered([1..130000],k->Sigma(k)<2*k);;  a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+3);

with(numtheory): A:=select(k->sigma(n)<2*k,[$1..130000]):
a:=select(j->A[j+1]=A[j]+3,[$1..nops(A)-1]);

Position[Differences[Select[Range[125000], DivisorSigma[1, #] < 2*# &]], 3] // Flatten (* Amiram Eldar, Mar 15 2024 *)

Sequence is { k | A005100(k+1) = A005101(k) + 3 }.

Sequence is { k | A125238(k) = 3 }.

cp's OEIS Frontend

A317044 Numbers k such that A(k+1) = A(k) + 1, where A() = A005100() are the deficient numbers.

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A317045 Numbers k such that A(k+1) = A(k) + 2, where A() = A005100() are the deficient numbers.

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GAP

Maple

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A317046 Numbers k such that A(k+1) = A(k) + 3, where A() = A005100() are the deficient numbers.

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Links

Crossrefs

Programs

GAP

Maple

Mathematica

Formula