Nels Olson - cp's OEIS frontend

A218072 Product of the nonzero digits (in base 10) of n^2.

1, 4, 9, 6, 10, 18, 36, 24, 8, 1, 2, 16, 54, 54, 20, 60, 144, 24, 18, 4, 16, 128, 90, 210, 60, 252, 126, 224, 32, 9, 54, 8, 72, 30, 20, 108, 162, 64, 10, 6, 48, 168, 288, 162, 20, 12, 36, 24, 8, 10, 12, 56, 144, 108, 30, 54, 216, 216, 96, 18, 42, 384, 1458

Offset: 1

Nels Olson, Oct 19 2012

			a(32) = 8 because 32*32 = 1024 and 1*2*4 = 8.

Similar to A053667, which does not exclude zero digits from the product.
Related to A218013.
Cf. A000290, A051801.

Table[Times@@(IntegerDigits[n^2]/.(0->1)),{n,120}] (* Harvey P. Dale, Dec 12 2017 *)

a(n) = {digs = digits(n^2); prod(i=1, #digs, if (digs[i], digs[i], 1));} \\ Michel Marcus, Aug 12 2013

a(n) = vecprod(select(x->(x>1), digits(n^2))); \\ Michel Marcus, Mar 07 2022

a(n) = A051801(n^2). - Michel Marcus, Mar 07 2022

A218029 Numbers that are equal to the product of the nonzero digits (in base 10) of their square.

Original entry on oeis.org

1, 30240, 60480, 51597803520, 687009790646587541893939200, 2639216811747930700939756830720000000, 399953837788563897626396208106026886244605021117749733129069000654848000000000

Offset: 1

Nels Olson, Oct 18 2012

			For n=30240, n^2 = 914,457,600; the product of the nonzero digits of this square, 9*1*4*4*5*7*6 = 30240 = n.

Special case of A218013 where the ratio of the digit-product to the original number is 1. Related to A218072.

A218013 Numbers that divide the product of the nonzero digits (in base 10) of their square.

Original entry on oeis.org

1, 2, 3, 5, 6, 8, 28, 36, 42, 54, 75, 192, 216, 288, 486, 525, 648, 768, 864, 882, 1728, 2160, 3024, 6048, 6075, 7056, 7680, 17280, 18144, 20736, 30240, 40824, 56448, 60480, 61236, 62208, 64512, 84672, 122472, 138915, 150528, 387072, 408240, 497664, 622080

Offset: 1

Nels Olson, Oct 18 2012

			For n=5, n^2 is 25; the product of the digits of 25 is 2 * 5 = 10, which is divisible by n=5.

David A. Corneth, Table of n, a(n) for n = 1..10919 (first 473 terms from Chai Wah Wu; terms <= 10^100)

Cf. A002473.

Related to A218072. Subsets of this sequence include A218029 and A218030.

isok(n) = digs = digits(n^2); (prod(i=1, #digs, if (digs[i], digs[i], 1)) % n) == 0; \\ Michel Marcus, Aug 12 2013

from operator import mul
from functools import reduce
from gmpy2 import t_mod, mpz
A218013 = [n for n in range(1,10**6) if not t_mod(reduce(mul,(mpz(d) for d in str(n**2) if d != '0')),n)] # Chai Wah Wu, Aug 23 2014

A218030 Numbers k equal to half of the product of the nonzero (base-10) digits of k^2.

Original entry on oeis.org

2, 5, 54, 648, 2160, 337169025526136832000, 685506275314921762068267522458966662115416623590907309075726336000000, 46641846972427276691124922228108091690332947069125333309512419901440000000000

Offset: 1

Nels Olson, Oct 18 2012

The first 5 terms of the sequence were found by the author around 1980 using his Commodore PET computer. He found the subsequent terms in 1991 by means of an improved program. The author has always referred to these as the "Faithy numbers" after his mother, Faith, who posed the problem.

			For n=5, n^2 is 25; the product of the digits of 25 is 2*5 = 10, which is equal to 2*n.

Michael S. Branicky, Table of n, a(n) for n = 1..12 (all terms < 10^300)
Michael S. Branicky, Python program.
Giovanni Resta, C program for this and related sequences.

Special case of A218013 where the ratio of the digit-product to the original number is 2. Related to A218072.

mx = 2^255; L = {};
p2 = 1; While[p2 < mx, Print["--> 2^", Log[2, p2]];
p3 = p2; While [p3 < mx,
  p5 = p3; While[p5 < mx,
   n = p5; While[n < mx,
    If[2 n == Times @@ Select[IntegerDigits[n^2], # > 0 &],
     AppendTo[L, n]; Print[n]]; n *= 7]; p5 *= 5]; p3 *= 3];
p2 *= 2]; Sort[L] (* Giovanni Resta, Oct 19 2012 *)

is_A218030(n)={my(d=digits(n^2));n*=2;for(i=1,#d,d[i]||next;n%d[i]&return;n\=d[i]);n==1} \\ M. F. Hasler, Oct 19 2012

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User: Nels Olson

A218072 Product of the nonzero digits (in base 10) of n^2.

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A218029 Numbers that are equal to the product of the nonzero digits (in base 10) of their square.

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A218013 Numbers that divide the product of the nonzero digits (in base 10) of their square.

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A218030 Numbers k equal to half of the product of the nonzero (base-10) digits of k^2.

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