A295042 - OEIS

%I #22 Apr 11 2021 16:14:22

%S 55959128224,68972878975,91653987424,171967420624,350441716624,

%T 372944997424,386136575824,711480344575,769856312224,789255692224,

%U 818564922175,997039218175,1071710665024,1216042052224,1340586071824,1925671372624,1954925637664,2045947528624

%N Numbers k such that both k and (k+1) are abundant, and neither is divisible by 3.

%C Subsequence of A096399.

%C All terms are of the form 3j+1, with j = 18653042741, 22990959658, 30551329141, 57322473541, 116813905541, 124314999141, 128712191941, 237160114858, 256618770741, 263085230741, 272854974058, 332346406058, ...

%H David A. Corneth, <a href="/A295042/b295042.txt">Table of n, a(n) for n = 1..988</a> (first 87 terms from Giovanni Resta)

%e k = 55959128224 is in the sequence as sigma(k) > 2*k and sigma(k + 1) > 2*(k + 1). - _David A. Corneth_, Apr 11 2021

%t abQ[n_] := Mod[n, 3] > 0 && DivisorSigma[1, n] > 2 n; abQ1[n_] := abQ[n - 1]; abQ2[n_] := abQ[n + 1]; s = Import["b115414.txt", "Data"][[All, -1]]; s1 = Select[s, abQ1] - 1; s2 = Select[s, abQ2]; seq = Union[s1, s2] (* using the b-File from A115414 *)

%o (PARI) isoka(n) = (n%3) && (sigma(n) > 2*n);

%o isok(n) = isoka(n) && isoka(n+1); \\ _Michel Marcus_, Nov 13 2017

%Y Cf. A005101, A096399, A115414.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 13 2017

%E a(13)-a(18) from _Giovanni Resta_, Aug 22 2018