A330880 -id:A330880 - cp's OEIS frontend

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

Scott R. Shannon, May 08 2020

			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.

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

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

Subsequence of A052382.

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

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

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.

Original entry on oeis.org

24, 36, 3276, 1886976

Offset: 1

Scott R. Shannon, May 12 2020

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

			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.

Cf. A007954, A049102, A085124.

Subsequence of A052382. Intersection of A334679 and A330880.

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

cp's OEIS Frontend

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.

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