A331813 - OEIS

%I #14 Feb 10 2020 06:42:56

%S 2,2,2,2,4,4,2,7,2,4,8,2,3,2,2,4,2,64,3,64,4,8,7,4,15,3,50,2,2,50,2,7,

%T 29184,2,16,64,4,16,4,385,15,9,313600,2,4,2793,4199,2,4,57600

%N a(n) is the least k > 1 such that k*A019278(n) belongs to A019278 too, or a(n) = 0 if no such k exists.

%C For the 132 terms (< 5*10^11) of the b-file for A019278, and using an extended list of terms, it can be checked that a(n) is not 0, even if the precise value is not known. For instance, a(51) <= 8097830664651.

%C Then a(52) to a(82) are: 4, 9, 1197, 8, 256, 4, 65155475, 64, 4096, 16, 195205791, 1387, 7, 37791, 4, 119, 8, 35136, 225, 64, 69127695, 2129920, 256, 4, 19671223, 9, 2, 1379763, 8, 90, 4096. And a(83) <= 7758260899200.

%C a(51) and a(83) are > 10^9.

%e With A019278 starting as 1, 2, 4, 8, 15, 16, 21, 24, 42, 60, 64, ...

%e one gets the proper multiples 2, 4, 8, 16, 60, 64, ...

%e and so the sequence begins: 2, 2, 2, 2, 4, 4, ...

%o (PARI) a(n, v019278) = my(m = v019278[n]); my(k=2, y = k*m); while (denominator(sigma(sigma(y))/y) != 1, k++; y += m); k;

%Y Cf. A019278 (integers m such that sigma(sigma(m))/m is an integer).

%K nonn,more

%O 1,1

%A _Michel Marcus_, Jan 27 2020