A069816 -id:A069816 - cp's OEIS frontend

A088116 Let n = abc..., where a, b, c, are digits of n. a(n) = abc...+bac...+c*ab...+..., i.e., a(n) = sum, over all the digits, of the product (number obtained by deleting a digit multiplied by the deleted digit).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 0, 14, 28, 42, 56, 70, 84, 98

Offset: 0

Amarnath Murthy, Sep 25 2003

First 100 terms (for all two digit numbers) match with that of A069816. A088116(10a + b) = 2ab = (a+b)^2 - (a^2 + b^2) = A069816(10a + b).

The first known fixed points, after zero, are numbers of the forms 36*10^k and 1314*10^k for k >= 0. All have 9 as the sum of their digits. Calculated up to n = 10^10. - Stéphane Rézel, Jul 31 2019

			a(1234) = 234 + 2*134 + 3*124 + 4*123 = 1366.

Jinyuan Wang, Table of n, a(n) for n = 0..10000

Cf. A069816, A087346, A088117.

Join[{0},Table[Total[IntegerDigits[n]Table[FromDigits[Drop[ IntegerDigits[ n],{d}]],{d,IntegerLength[n]}]],{n,100}]] (* Harvey P. Dale, Dec 23 2021 *)

a(n) = {v=digits(n);sum(k=1,#v,v[k]*(n\10^(#v-k+1)*10^(#v-k)+n%10^(#v-k)));} \\ Jinyuan Wang, Aug 01 2019

More terms from David Wasserman, May 10 2005

Offset 0 from Stéphane Rézel, Jul 31 2019

A069939 1/3!((Sum of digits of n)^3 + 3(Sum of digits of n)(Sum of digits^2 of n) + 2(Sum of digits^3 of n)).

Original entry on oeis.org

0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1, 4, 15, 40, 85, 156, 259, 400, 585, 820, 8, 15, 32, 65, 120, 203, 320, 477, 680, 935, 27, 40, 65, 108, 175, 272, 405, 580, 803, 1080, 64, 85, 120, 175, 256, 369, 520, 715, 960, 1261, 125, 156, 203, 272, 369, 500, 671

Offset: 0

Vladeta Jovovic, May 04 2002

Cf. A007953, A003132, A055012, A069816.

sdn[n_]:=Module[{c=1/3!,idn=IntegerDigits[n],sdn},sdn=Total[idn];c(sdn^3+ 3sdn Total[idn^2]+2Total[idn^3])]; Array[sdn,60,0] (* Harvey P. Dale, Dec 29 2011 *)

A069940 (1/2)*((Sum of digits of n)^2 + (Sum of digits^2 of n)).

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 4, 7, 12, 19, 28, 39, 52, 67, 84, 103, 9, 13, 19, 27, 37, 49, 63, 79, 97, 117, 16, 21, 28, 37, 48, 61, 76, 93, 112, 133, 25, 31, 39, 49, 61, 75, 91, 109, 129, 151, 36, 43, 52, 63, 76, 91, 108, 127

Offset: 0

Vladeta Jovovic, May 04 2002

Cf. A069816, A007953, A003132.

cp's OEIS Frontend

A088116 Let n = abc..., where a, b, c, are digits of n. a(n) = abc...+bac...+c*ab...+..., i.e., a(n) = sum, over all the digits, of the product (number obtained by deleting a digit multiplied by the deleted digit).

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A069939 1/3!((Sum of digits of n)^3 + 3(Sum of digits of n)(Sum of digits^2 of n) + 2(Sum of digits^3 of n)).

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A069940 (1/2)*((Sum of digits of n)^2 + (Sum of digits^2 of n)).

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cp's OEIS Frontend

A088116 Let n = abc..., where a, b, c, are digits of n. a(n) = a*bc...+b*ac...+c*ab...+..., i.e., a(n) = sum, over all the digits, of the product (number obtained by deleting a digit multiplied by the deleted digit).

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A069939 1/3!*((Sum of digits of n)^3 + 3*(Sum of digits of n)*(Sum of digits^2 of n) + 2*(Sum of digits^3 of n)).

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A069940 (1/2)*((Sum of digits of n)^2 + (Sum of digits^2 of n)).

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Author

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A088116 Let n = abc..., where a, b, c, are digits of n. a(n) = abc...+bac...+c*ab...+..., i.e., a(n) = sum, over all the digits, of the product (number obtained by deleting a digit multiplied by the deleted digit).

A069939 1/3!((Sum of digits of n)^3 + 3(Sum of digits of n)(Sum of digits^2 of n) + 2(Sum of digits^3 of n)).