A053667 -id:A053667 - cp's OEIS frontend

A248648 The squares related to the strictly increasing subsequence of A053667(n), n >= 1.

1, 4, 9, 25, 36, 49, 169, 256, 289, 576, 676, 1849, 3844, 3969, 5776, 6889, 26896, 27889, 55696, 69696, 97969, 339889, 376996, 499849, 678976, 698896, 779689, 2679769, 2768896, 2778889, 4695889, 4999696, 9696996, 26697889, 28879876, 36759969, 37994896

Offset: 1

K. D. Bajpai, Oct 10 2014

The triangular numbers of this form are at A246753.

			5 * 5 = 25 is a square and the product of its digits = 2 * 5 = 10. Because a(3) = 9, and 4 * 4 = 16 has product of digits 6 < 9, a(4) = 25 because 10 > 9. The next entry a(5) comes from 6 * 6 = 36 with product of digits 18 > 10.
From _Wolfdieter Lang_, Oct 31 2014: (Start)
A053667 is sieved (from the left to the right):
1, 2, 3, 4,  5,  6,  7,  8, 9, 10, 11, 12, 13, 14, ...
1, 4, 9, 6, 10, 18, 36, 24, 8,  0,  2, 16, 54, 54, ...
1, 4, 9, x, 10, 18, 36,  x, x,  x,  x,  x, 54,  x, ...
and the related leftover squares are
1, 4, 9,    25  36, 49,                    169,    ...
(End)
-------------------------------------------------------

K. D. Bajpai, Table of n, a(n) for n = 1..116

Cf. A000290, A230041, A246569, A246753, A053667.

A248648 = {}; k = 0; Do[s = Apply[Times, IntegerDigits[n^2]];If[s > k, k = s; AppendTo[A248648, n^2]], {n, 1, 10^4}]; A248648

product=0;for(n=1,10^5,d=digits(n^2);p=prod(i=1,#d,d[i]);while(p>product,print1(n^2,", ");product=p)) \\ Derek Orr, Oct 11 2014

Edited, Name specified, example reformulated, A053667 and 'easy' added. - Wolfdieter Lang, Oct 31 2014

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

Original entry on oeis.org

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

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A248648 The squares related to the strictly increasing subsequence of A053667(n), n >= 1.

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

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