A296027 Numbers k such that k | (sigma(k-2) + sigma(k-1) + sigma(k+1) + sigma(k+2)).

6, 57, 443, 1407, 1410, 12242, 15051, 30952, 44277, 65190, 68697, 609531, 921774, 951092, 2012670, 2820460, 11961680, 32886944, 3450005970

Offset: 1

Author

Paolo P. Lava, Dec 04 2017

Keywords

• nonn
• more

Comments

Values of the ratio ( sigma(k-2)+sigma(k-1)+sigma(k+1)+sigma(k+2) ) / k: 6, 6, 7, 6, 6, 8, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, ...

Examples

			6 is in the sequence because (sigma(4) + sigma(5) + sigma(7) + sigma(8))/6 = (7 + 6 + 8 + 15)/6 = 6;
443 is in the sequence because (sigma(441) + sigma(442) + sigma(444) + sigma(445))/443 = (741 + 756 + 1064 + 540)/443 = 7.
		

Crossrefs

Cf. A186103, A227306.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,c,d,f,k,n;
a:=sigma(0); b:=sigma(1); c:=sigma(2); d:=sigma(3); f:=sigma(4);
for n from 2 to q do if type((a+b+d+f)/n,integer) then print(n,(a+b+d+f)/n); fi; a:=b; b:=c; c:=d; d:=f; f:=sigma(n+3); od; end: P(10^9);

PARI

lista(nn) = {my(v = vector(nn, k, sigma(k))); for (k=3, nn-3, if (!((v[k-2]+v[k-1]+v[k+1]+v[k+2]) % k), print1(k, ", ")););} \\ Michel Marcus, Sep 10 2019

PARI

upto(n) = my(v=List(vector(5,i,sigma(i))), res=List()); for(i=6, n, if((v[1] + v[2] + v[4] + v[5]) % (i-3) == 0, listput(res, i-3)); listpop(v,1); listput(v,sigma(i))); res \\ David A. Corneth, Sep 10 2019

Extensions

Term 2 removed and a(17)-a(18) added by Michel Marcus, Sep 10 2019

a(19) from Daniel Suteu, Sep 10 2019