A334679 Numbers k such that k*p is divisible by k+p, where p > 0 and p = A007954(k) = the product of digits of k.

2, 4, 6, 8, 24, 36, 63, 456, 495, 3276, 6624, 7497, 8832, 19728, 23976, 127488, 167328, 273525, 274995, 297675, 576975, 661248, 797769, 853776, 1323648, 1378272, 1491264, 1886976, 3483648, 3679263, 3787749, 4644864, 6386688, 7886592, 7888896, 12841472, 15974784, 16224768

Offset: 1

Author

Scott R. Shannon, May 08 2020

Keywords

• nonn
• base

Examples

			8 is a term as p = 8 and 8*8 = 64 is divisible by 8+8 = 16.
3276 is a term as p = 3*2*7*6 = 252 and 3276*252 = 825552 is divisible by 3276+252 = 3528.
3787749 is a term as p = 3*7*8*7*7*4*9 = 296352 and 3787749*296352 = 1122506991648 is divisible by 3787749+296352 = 4084101.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..95 (terms < 3.5*10^14)

Crossrefs

Cf. A330880, A334803, A007954, A049102, A085124.

Subsequence of A052382.

Programs

Mathematica

Select[Range[10^6], (p = Times @@ IntegerDigits@ #; p > 0 && Mod[# p, # + p] == 0) &] (* Giovanni Resta, May 08 2020 *)

PARI

isok(m) = my(p=vecprod(digits(m))); p && !((m*p) % (m+p)); \\ Michel Marcus, May 08 2020