A078156 -id:A078156 - cp's OEIS frontend

A078155 A078152(n!).

0, 0, 0, 0, 4, 22, 80, 304, 1043, 3538, 12094, 42979, 156237, 587926, 2283038, 9142910, 37708601, 160014979, 697523776, 3119511496, 14295524835, 67052144163, 321571055089, 1575370699764, 7876854373196, 40164235356266, 208699490940770

Offset: 1

Labos Elemer, Nov 27 2002

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..807

Cf. A078152, A078153, A078154, A078156, A078157, A078158.

Table[ Length[ Union[ Table[ Floor[w!/j], {j, 1, w!}]]] - DivisorSigma[0, w! ], {w, 1, 11}]
(* Second program: *)
Array[Floor@ Sqrt[4 # + 1] - 1 - DivisorSigma[0, #] &[#!] &, 27] (* Michael De Vlieger, Dec 13 2018 *)

a(n) = A078152(n!) = A055086(n!) - A000005(n!).

Extended by Robert G. Wilson v, Dec 02 2002

a(11) corrected and terms a(12) onward added by Max Alekseyev, Feb 12 2012

A078157 a(n) = A078152(2^n).

Original entry on oeis.org

0, 0, 0, 2, 4, 8, 13, 22, 34, 52, 77, 114, 166, 240, 345, 494, 705, 1004, 1427, 2026, 2873, 4072, 5767, 8166, 11558, 16356, 23141, 32738, 46309, 65504, 92648, 131038, 185328, 262108, 370690, 524250, 741416, 1048536, 1482869, 2097110, 2965777

Offset: 1

Labos Elemer, Nov 27 2002

nonn

Cf. A078152, A078153, A078154, A078155, A078156, A078158.

For n>1, a(n) = floor(sqrt(2^(n+2))) - n - 2

Extended by Robert G. Wilson v, Dec 02 2002

More terms from Max Alekseyev, Feb 12 2012

A078158 a(n) = A078153(2^n).

Original entry on oeis.org

0, 0, 0, 8, 24, 73, 183, 470, 1112, 2592, 5876, 13233, 29316, 64329, 140028, 302824, 651101, 1393204, 2968129, 6300084, 13326815, 28108564, 59123162, 124065274, 259759346, 542781169, 1132075405, 2357197804, 4900443545, 10173068455, 21090365684

Offset: 1

Labos Elemer, Nov 27 2002

nonn

Cf. A078152, A078153, A078154, A078155, A078156, A078157.

Table[ Apply[ Plus, Union[ Table[ Floor[2^w/j], {j, 1, 2^w}]]] - DivisorSigma[1, 2^w], {w, 1, 24}]

Extended by Robert G. Wilson v, Dec 02 2002

Terms a(26) onward from Max Alekseyev, Feb 12 2012

cp's OEIS Frontend

A078155 A078152(n!).

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A078157 a(n) = A078152(2^n).

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Author

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Formula

Extensions

A078158 a(n) = A078153(2^n).

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Author

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Mathematica

Extensions