A334803 Numbers k such that k*p is divisible by k+p and k-p, where k > p > 0 and p = A007954(k) = the product of digits of k.

24, 36, 3276, 1886976

Offset: 1

Author

Scott R. Shannon, May 12 2020

Keywords

• nonn
• base
• more

Comments

If a(5) exists it is at least 3*10^12.

a(5) > 1.5*10^14, if it exists. - Giovanni Resta, May 12 2020

Examples

			24 is a term as p = 2*4 = 8 and 24*8 = 192 is divisible by both 24-8 = 16 and 24+8 = 32.
36 is a term as p = 3*6 = 18 and 38*18 = 648 is divisible by both 36-18 = 18 and 36+18 = 54.
3276 is a term as p = 3*2*7*6 = 252 and 3276*252 = 825552 is divisible by both 3276-252 = 3024 and 3276+252 = 3528.
1886976 is a term as p = 1*8*8*6*9*7*6 = 145152 and 1886976*145152 = 273898340352 is divisible by both 1886976-145152 = 1741824 and 1886976+145152 = 2032128.
		

Crossrefs

Cf. A007954, A049102, A085124.

Subsequence of A052382. Intersection of A334679 and A330880.

Programs

PARI

isok(m) = my(p=vecprod(digits(m))); p && (m-p) && !((m*p) % (m-p)) && !((m*p) % (m+p)); \\ Michel Marcus, May 12 2020