A098114 -id:A098114 - cp's OEIS frontend

A097372 Numbers n such that n=(d_1+6)(d_2+6)...*(d_k+6) where d_1 d_2 ... d_k is the decimal expansion of n.

90, 840, 4320, 59400, 60480, 917280, 2419200, 34992000, 3714984000, 460522782720, 896168448000, 2194698240000, 39109522636800, 229419122688000, 239446056960000, 650997662515200, 3954407288832000, 182279345504256000, 883270791696384000, 275333274192936960000

Offset: 1

Farideh Firoozbakht, Sep 21 2004

			90 is in the sequence because 90 = (9+6)*(0+6).

Hiroaki Yamanouchi and Max Alekseyev, Table of n, a(n) for n = 1..29 (contains all terms below 10^100)

Cf. A097371, A098681, A098682.

Cf. A098113, A098114, A097371, A115227.

Do[h=IntegerDigits[n];l=Length[h];If[n==Product[h[[k]]+6, {k, l}], Print[n]], {n, 130000000}]

More terms from Giovanni Resta, Jan 16 2006
a(19)-a(24) from Hiroaki Yamanouchi, Sep 08 2014
a(25)-a(29) from Max Alekseyev, Jan 25 2015

A055482 There exists some k>0 such that n is the product of (k + digits of n).

Original entry on oeis.org

12, 18, 24, 35, 50, 56, 90, 120, 210, 315, 450, 780, 840, 1500, 3920, 4320, 4752, 7744, 16500, 24960, 57915, 59400, 60480, 91728, 269500, 493920, 917280, 1293600, 2419200, 3386880, 34992000, 266378112, 317447424, 1277337600, 3714984000, 14948388000, 48697248600, 460522782720, 896168448000

Offset: 1

Erich Friedman, Jun 27 2000

18 appears to be the only term with k=1, there are no other terms with k=1 as well as with k=3,8,9 below 10^100. - Max Alekseyev, Jan 25 2015

			4752 = (4+4)(4+7)(4+5)(4+2).

Giovanni Resta, Table of n, a(n) for n = 1..59 (terms < 10^38)

Cf. A055481, A113756

Subsequences: A098113 (k=2), A098114 (k=4), A097371 (k=5), A097372 (k=6), A115227 (k=7)

L={}; Do[Print@ n; Do[p = Reverse/@ IntegerPartitions[ k, {n}, Range[0, 9]]; Do[z = Times@@ (e + k); If[ Sort@ IntegerDigits@ z == e, Print[{z, k}]; AppendTo[L, z]], {k, 9}, {e, p}], {k, 9*n}],{n, 2, 13}]; Sort@ L (* terms < 10^13, Giovanni Resta, Jul 24 2015 *)

Offset corrected and more terms added by Max Alekseyev, Jan 23 2015

A098113 Numbers n such that n=(d_1+2)(d_2+2)...*(d_k+2) where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

12, 24, 35, 56

Offset: 1

Farideh Firoozbakht, Sep 24 2004

It seems that there are no further terms.

No other terms below 10^150. - Max Alekseyev, Jan 25 2015

			56 is in the sequence because 56=(5+2)*(6+2).

Cf. A098114, A097371, A097372.

Do[d=IntegerDigits[n];k=Length[d];If[n==Product[d[[j]]+2, {j, k}], Print[n]], {n, 10000000}]

A115227 Numbers k such that k = (d_1+7)(d_2+7)...(d_m+7) where d_1 d_2 ... d_m is the decimal expansion of k.

Original entry on oeis.org

8314460009856000, 31746120037632000, 92632873013093597184000000, 1108240107492643314063114240000, 25425833233403394290952098021376000000000, 67839608823081187608930897100800000000000, 1064102035269050218905833606927320350720000000

Offset: 1

Giovanni Resta, Jan 16 2006

			a(1) = 8314460009856000 = (7+8)*(7+3)*(7+1)*...*(7+6)*(7+0)*(7+0)*(7+0).

Max Alekseyev, Table of n, a(n) for n = 1..18 (contains all terms below 10^100)
Jean-Marie De Koninck, Those Fascinating Numbers, Amer. Math. Soc., (2009), page 377.

Cf. A055482, A098113, A098114, A097371, A097372, A113756

a(6)-a(18) from Max Alekseyev, Jan 25 2015

A113756 Numbers n>9 such that n=Abs[(c+d_1)(c+d_2)...*(c+d_k)] where d_1 d_2 ... d_k is the decimal expansion of n and c is an integer constant.

Original entry on oeis.org

12, 18, 24, 35, 50, 56, 90, 100, 120, 180, 210, 315, 350, 450, 500, 672, 728, 780, 840, 910, 1500, 1800, 3150, 3500, 3920, 4320, 4752, 5000, 7056, 7200, 7744, 8960, 16500, 18000, 19008, 24960, 31500, 35000, 50000, 57915, 59400, 60480, 67392, 91728

Offset: 1

Giovanni Resta, Jan 17 2006

Some entries, namely 12, 18, 24, 35, 50, 56, 90, 120, 210, 315, 840, 4752, 7744, 917280 (up to 10^20), have 2 representations, e.g., 840 for c=6 and c=-14 or 917280 for c=6 and c=-15. Sequence is infinite since contains 35*10^k, 315*10^k, 18*10^k and 5*10^k, for k>=0 and c=-10.

			315 belongs since 315=|(4+3)(4+1)(4+5)|
728 belongs since 728=|(-15+7)(-15+2)(-15+8)|

Cf. A055482, A115227, A098113, A098114, A097371, A097372.

L = {}; Do[d = IntegerDigits@n; Do[If[n == Abs[Times @@ (d + c)], AppendTo[L, {n, c}]; Print[{n, c}]], {c, -19, 10}], {n, 10, 1000000}]; Print[Union[Transpose[L][[1]]]]; L

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A097372 Numbers n such that n=(d_1+6)*(d_2+6)*...*(d_k+6) where d_1 d_2 ... d_k is the decimal expansion of n.

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A055482 There exists some k>0 such that n is the product of (k + digits of n).

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A098113 Numbers n such that n=(d_1+2)*(d_2+2)*...*(d_k+2) where d_1 d_2 ... d_k is the decimal expansion of n.

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A115227 Numbers k such that k = (d_1+7)(d_2+7)*...*(d_m+7) where d_1 d_2 ... d_m is the decimal expansion of k.

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A113756 Numbers n>9 such that n=Abs[(c+d_1)*(c+d_2)*...*(c+d_k)] where d_1 d_2 ... d_k is the decimal expansion of n and c is an integer constant.

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A097372 Numbers n such that n=(d_1+6)(d_2+6)...*(d_k+6) where d_1 d_2 ... d_k is the decimal expansion of n.

A098113 Numbers n such that n=(d_1+2)(d_2+2)...*(d_k+2) where d_1 d_2 ... d_k is the decimal expansion of n.

A115227 Numbers k such that k = (d_1+7)(d_2+7)...(d_m+7) where d_1 d_2 ... d_m is the decimal expansion of k.

A113756 Numbers n>9 such that n=Abs[(c+d_1)(c+d_2)...*(c+d_k)] where d_1 d_2 ... d_k is the decimal expansion of n and c is an integer constant.