A104149 -id:A104149 - cp's OEIS frontend

A065900 Numbers n such that sigma(n) = sigma(n-1) + sigma(n-2).

3, 4, 24, 1968, 3264, 5016, 60456, 1016508, 4420164, 12055512, 14365608, 25726728, 27896424, 66562308, 72764736, 98734968, 175186656, 224868312, 253694928, 288657204, 386668344, 421575408, 504737748, 630645456, 1493548000, 1653797796, 2120325012, 2221315152

Offset: 1

Jason Earls, Dec 07 2001

nonn

No other terms less than 1000000000. - Sam Handler (sam_5_5_5_0(AT)yahoo.com), Nov 23 2004

Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..112 (terms < 10^13, first 50 terms from Donovan Johnson)

Cf. A000203, A076530, A104149.

s1=1; s2=3; for(n=3, 10^8, s3=sigma(n); if(s3==s1+s2, print1(n ", ")); s1=s2; s2=s3) /* Donovan Johnson, Apr 06 2013 */

a(n) = A076530(n) + 1 = A104149(n) + 2. - Alex Ratushnyak, Jul 06 2013

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Nov 23 2004

A076530 Numbers n such that sigma(n) = sigma(n+1) - sigma(n-1).

Original entry on oeis.org

2, 3, 23, 1967, 3263, 5015, 60455, 1016507, 4420163, 12055511, 14365607, 25726727, 27896423, 66562307, 72764735, 98734967, 175186655, 224868311, 253694927, 288657203, 386668343, 421575407, 504737747, 630645455, 1493547999

Offset: 1

Joseph L. Pe, Oct 18 2002

nonn

			sigma(24) = 60. sigma(23) = 24. sigma(22) = 36 and 24 = 60 - 36; hence 23 is a term of the sequence.

Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..112 (terms < 10^13, first 50 terms from Donovan Johnson)

Cf. A000203, A065900, A104149.

Select[Range[2, 10^5], DivisorSigma[1, # ] == DivisorSigma[1, # + 1] - DivisorSigma[1, # - 1] &]
Flatten[Position[Partition[DivisorSigma[1,Range[1493548000]],3,1],?(#[[2]] == #[[3]]-#[[1]]&),1,Heads->False]]+1 (* _Harvey P. Dale, Apr 13 2020 *)

a(n) = A065900(n) - 1 = A104149(n) + 1. - Alex Ratushnyak, Jul 06 2013

a(8)-a(25) from Donovan Johnson, Feb 01 2009

A348335 a(n) = smallest k such that the sum of the divisors of the n numbers from k to k+n-1 equals sigma(k+n), or -1 if no such k exists.

Original entry on oeis.org

14, 1, 591357

Offset: 1

Metin Sariyar, Oct 13 2021

a(4) > 10^9, if it exists. - Amiram Eldar, Oct 13 2021

			a(1) = 14 because sigma(14) = sigma(15) = 24; a(1) = A002961(1).
a(2) = 1 because sigma(1) + sigma(2) = 1 + 3 = 4, the same as sigma(3) = 4; a(2) = A104149(1).
a(3) = 591357 because sigma(591357) + sigma(591358) + sigma(591359) = 866880 + 890352 + 599760 = 2356992, the same as sigma(591360) = 2356992.

Cf. A000203, A002961, A065900, A092403, A104149, A252922.

a[n_] := Module[{sig = DivisorSigma[1, Range[n]], k = n + 1}, While[(s = DivisorSigma[1, k]) != Plus @@ sig, sig = Join[Drop[sig, 1], {s}]; k++]; k - n]; Array[a, 3] (* Amiram Eldar, Oct 29 2021 *)

isok(m, nb) = sum(i=1, nb, sigma(m+i-1)) == sigma(m+nb);
a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, Oct 28 2021

A348689 a(n) = sigma(n) + sigma(n+1) - sigma(n+2), where sigma is the sum of divisors.

Original entry on oeis.org

0, 0, 5, 1, 10, 5, 10, 10, 19, 2, 26, 18, 14, 17, 37, 10, 37, 17, 30, 38, 44, 0, 53, 49, 33, 26, 66, 14, 70, 41, 47, 57, 54, 11, 101, 69, 42, 26, 104, 36, 94, 56, 50, 90, 102, -4, 115, 88, 78, 67, 116, 32, 102, 72, 112, 110, 110, -18, 166, 134, 54, 73, 147, 67, 160, 86, 98, 78, 168, 21

Offset: 1

Michel Marcus, Oct 29 2021

sign

Michel Marcus, Table of n, a(n) for n = 1..10000

Cf. A000203, A104149, A348688.

Array[#+#2-#3&@@DivisorSigma[1,{#,#+1,#+2}]&,100] (* Giorgos Kalogeropoulos, Oct 29 2021 *)

a(n) = sigma(n)+sigma(n+1) - sigma(n+2);

cp's OEIS Frontend

A065900 Numbers n such that sigma(n) = sigma(n-1) + sigma(n-2).

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A076530 Numbers n such that sigma(n) = sigma(n+1) - sigma(n-1).

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A348335 a(n) = smallest k such that the sum of the divisors of the n numbers from k to k+n-1 equals sigma(k+n), or -1 if no such k exists.

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A348689 a(n) = sigma(n) + sigma(n+1) - sigma(n+2), where sigma is the sum of divisors.

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Mathematica

PARI