A295042 Numbers k such that both k and (k+1) are abundant, and neither is divisible by 3.

55959128224, 68972878975, 91653987424, 171967420624, 350441716624, 372944997424, 386136575824, 711480344575, 769856312224, 789255692224, 818564922175, 997039218175, 1071710665024, 1216042052224, 1340586071824, 1925671372624, 1954925637664, 2045947528624

Offset: 1

Author

Amiram Eldar, Nov 13 2017

Keywords

• nonn

Comments

Subsequence of A096399.

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

Examples

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

Links

• David A. Corneth, Table of n, a(n) for n = 1..988 (first 87 terms from Giovanni Resta)

Crossrefs

Cf. A005101, A096399, A115414.

Programs

Mathematica

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 *)

PARI

isoka(n) = (n%3) && (sigma(n) > 2*n);
isok(n) = isoka(n) && isoka(n+1); \\ Michel Marcus, Nov 13 2017

Extensions

a(13)-a(18) from Giovanni Resta, Aug 22 2018