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A375819
Numbers k such that the sum of the numbers from 1 to k and that from 1 to k+1 share the same sum of divisors.
1
28, 33, 412, 1914, 2668, 2728, 2913, 3268, 4187, 5370, 5948, 7169, 8728, 9359, 12565, 15085, 21461, 24881, 25019, 26609, 29682, 37746, 38716, 40290, 46863, 49225, 49914, 51835, 53963, 59987, 67996, 73132, 77057, 81055, 85636, 101101, 113128, 127585, 129330, 143369
OFFSET
1,1
COMMENTS
The sequence gives the index of the first element of a pair of consecutive triangular numbers with the same sum of divisors.
The even terms of this sequence are exactly twice the terms of A002961. - Amiram Eldar, Sep 16 2024
FORMULA
A000203(A000217(a(n))) = A000203(A000217(a(n)+1)).
EXAMPLE
Sum of the numbers from 1 to 28 -> 406; from 1 to 29 -> 435;
sigma(406) = sigma(435) = 720.
MAPLE
with(numtheory): P:=proc(q) local a, j, n, t; j:=[]; t:=0;
for n from 1 to q do a:=n*(n+1)/2; if sigma(a)=t then j:=[op(j), n-1]; fi;
t:=sigma(a); od; op(j); end: P(143370);
MATHEMATICA
Select[Range[145000], DivisorSigma[1, #(#+1)/2]==DivisorSigma[1, (#+1)(#+2)/2] &] (* Stefano Spezia, Sep 16 2024 *)
PROG
(Python)
from itertools import count, islice
from sympy import divisor_sigma
def A375819_gen(): # generator of terms
s, a = 1, 1
return (k-1 for k in count(2) if a==(a:=divisor_sigma(s:=s+k)))
A375819_list = list(islice(A375819_gen(), 10)) # Chai Wah Wu, Oct 14 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Sep 16 2024
STATUS
approved